POSITION ESTIMATION USING A NETWORK OF GLOBAL-POSITIONING RECEIVERS

Description

FIELD OF THE INVENTION

[0001] The present invention relates to estimating precise position of a stationary or moving object using multiple satellite signals and a network of multiple receivers. The present invention is particularly suited to position estimation in real-time kinetic environments where it is desirable to take into account the spatial distribution of the ionosphere delay.

BACKGROUND OF THE INVENTION

[0002] Satellite navigation systems, such as GPS (USA) and GLONASS (Russia), are intended for accuracy self-positioning of different users possessing special navigation receivers. A navigation receiver receives and processes radio signals broadcast by satellites located within line-of-sight distance, and from this, computes the position of the receiver within a pre-defined coordinate system. However, for military reasons, the most accurate parts of these satellite signals are encrypted with codes only known to military users. Civilian users cannot access the most accurate parts of the satellite signals, which makes it difficult for civilian users to achieve accurate results. In addition, there are sources of noise and error that degrade the accuracy of the satellite signals, and consequently reduce the accuracy of computed values of position. Such sources include carrier ambiguities, receiver time offsets, and atmospheric effects on the satellite signals.

[0003] The present invention is directed to increasing the accuracy of estimating the position of a rover station in view of carrier ambiguities, receiver time offsets, and atmospheric effects.

SUMMARY OF THE INVENTION

[0004] The present invention relates to a method and apparatus for determining the position of a receiver (e.g., rover) with respect to the positions of at least two other receivers (e.g., base receivers) which are located at known positions. The knowledge of the precise locations of the at least two other receivers (located at known positions within the coordinate system) makes it possible to better account for one or all of carrier ambiguities, receiver time offsets, and atmospheric effects encountered by the rover receiver, and to thereby increase the accuracy of the estimated receiver position of the rover (e.g., rover position).

[0005] In a first aspect of the present invention, an exemplary apparatus/method comprises receiving the known locations of a first base station and a second base station, obtaining a time offset representative of the time difference between the clocks of the first and second base stations, and obtaining measured satellite data as received by the rover, the first base station, and the second base station. The measured satellite data comprises pseudo-range information. The exemplary apparatus/method generates a first set of residuals of differential navigation equations associated with a set of measured pseudo-ranges related to a first baseline (R-B1) between the rover and the first base station. The residuals are related to the measured satellite data received by the rover station and the first base station, the locations of the satellites, and the locations of the rover station and the first base station. The exemplary apparatus/method also generates a second set of residuals of differential navigation equations associated with a set of measure pseudo-ranges related to a second baseline (R-B2) between the rover and the second base station. These residuals are related to the measured satellite data received by the rover station and the second base station, the locations of the satellites, and the locations of the rover station and the second base station. The exemplary apparatus/method estimates the rover's location from the first set of residuals, the second set of residuals, the time offset between the clocks of the first and second base stations.

[0006] In a second aspect of the present invention, the position information and measured satellite data from a third base station are received. Also, a time offset representative of the time difference between the clocks of the first and third base stations is obtained. Thereafter, the exemplary apparatus/method also generates a third set of residuals of differential navigation equations associated with a set of measured pseudo-ranges related to a third baseline (R-B3) between the rover and the third base station, and estimates the rover's location further with the third set of residuals and the time offset between the clocks of the first and third base stations.

[0007] In a third aspect of the present invention, which may be applied with any of the aspects of the present invention described herein, the exemplary apparatus/method generates the time offset(s) for the base stations from the measured satellite data of the base stations provided to it.

[0008] In a fourth aspect of the present invention, which may be applied with any of the aspects of the present invention described herein, the exemplary apparatus/method obtains measured satellite carrier phase data as received by the rover and the first base station (the first base line). The exemplary apparatus/method generates a fourth set of residuals of differential navigation equations associated with a set of measured carrier phase data related to the first base line, and resolves the cycle ambiguities in the carrier phase data from the fourth residual and one or more of the first, second, and third residuals. The resolved cycle ambiguities may take the form of floating ambiguities, fixed-integer ambiguities, and/or integer ambiguities. The exemplary apparatus/method estimates the rover's location further with the fourth set of residuals and the resolved cycle ambiguities associated with the first base line.

[0009] In a fifth aspect of the present invention, which may be applied with any of the aspects of the present invention described herein, the exemplary apparatus/method obtains measured satellite carrier phase data as received by the second base station, and further obtains a set of cycle ambiguities related to a set of satellite phase measurements associated with the baseline between the first and second base stations (B1-B2). The exemplary apparatus/method generates a fifth set of residuals of differential navigation equations associated with a set of measured carrier phase data related to the second base line between the rover and the second base station (R-B2), and resolves the cycle ambiguities in the carrier phase data from the fifth residual, the set of cycle ambiguities associated with the baseline between the first and second base stations, and one or more of the first, second, third, and fourth residuals. The resolved cycle ambiguities may take the form of floating ambiguities, fixed-integer ambiguities, and/or integer ambiguities. The exemplary apparatus/method estimates the rover's location further with the fifth set of residuals and the resolved cycle ambiguities associated with the second base line (R-B2).

[0010] In a sixth aspect of the present invention, which may be applied with any of the aspects of the present invention described herein, the exemplary apparatus/method receives measured satellite carrier phase data as received by the third base station, and further obtains a set of cycle ambiguities related to a set of satellite phase measurements associated with the baseline between the first and third base stations (B1-B3). The exemplary apparatus/method generates a sixth set of residuals of differential navigation equations associated with a set of measured carrier phase data related to the third base line between the rover and the third base station (R-B3), and resolves the cycle ambiguities in the carrier phase data from the sixth residual, the set of cycle ambiguities associated with the baseline between the first and third base stations, and one or more of the first, second, third, fourth, and fifth residuals. The resolved cycle ambiguities may take the form of floating ambiguities, fixed-integer ambiguities, and/or integer ambiguities. The exemplary apparatus/method estimates the rover's location further with the sixth set of residuals and the resolved cycle ambiguities associated with the third base line (R-B3).

[0011] In a seventh aspect of the present invention, which may be applied with any of the aspects of the present invention described herein, the exemplary apparatus/method obtains a first set of first ionosphere delay differentials associated with the satellite signals received along the base line formed by the first and second base stations, and generates ionosphere delay corrections to one or more of the above-described first through sixth residuals from the first set of first ionosphere delay differentials, the locations of the first and second base stations, and an estimated location of the rover station. As a further option, the exemplary apparatus/method obtains set of second ionosphere delay differentials associated with the satellite signals received along the base line formed by the first and third base stations (or the base line formed by the second and third base stations), and generates the ionosphere delay corrections to the one or more of the above-described first through sixth residuals further from the second set of ionosphere delay differentials and the location of the third base station.

[0012] In an eight aspect of the present invention, which may be applied to the seventh and further aspects of the present invention described herein, the exemplary apparatus/method forms one or more of the first through sixth residuals to account for second order effects in the ionosphere delay corrections applied to the baselines associated with the rover, and further generates an estimate of the second order effects.

[0013] In a ninth aspect of the present invention, which may be applied with any of the aspects of the present invention described herein, the exemplary apparatus/method generates the time offset representative of the time difference between the clocks of the first and second base stations, and optionally the time offset representative of the time difference between the clocks of the first and third base stations. As a further option, the apparatus/method generates the time offset representative of the time difference between the clocks of the second and third base stations, and performs a consistency check of the time offsets.

[0014] In an tenth aspect of the present invention, which may be applied with several of the aspects of the present invention described herein, the exemplary apparatus/method generates the resolved cycle ambiguities associated with the baseline between the first and second base stations (B1-B2), and optionally generates the resolved cycle ambiguities associated with the baseline between the first and third base stations (B1-B3). As a further option, the apparatus/method generates the resolved cycle ambiguities associated with the baseline between the second and third base stations (B2-B3), and performs a consistency check of the cycle ambiguities associated with the baselines between the base stations.

[0015] In an eleventh aspect of the present invention, which may be applied with any aspects of the present invention described herein which account for ionosphere delays, the exemplary apparatus/method generates the first set of first ionosphere delay differentials, and optionally the second set of first ionosphere delay differentials. As a further option, the apparatus/method generates a third set of ionosphere delay differentials associated with the satellite signals received along the base line formed by the second and third base stations, and generates therefrom three sets of ionosphere delay differentials which are self consistent.

[0016] Accordingly, it is an object of the present invention to increase the accuracy of estimating the rover's position using information from one or more baselines associated with two or more base stations.

[0017] It is a further object of the present invention to enable the spacing between the rover and the base stations to increase while maintaining or improving the accuracy of the estimation of the rover's position.

[0018] These and other objects of the present invention will become apparent to those skilled in the art from the following detailed description of the invention, the accompanying drawings, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] 

FIG. 1 is a perspective view of a rover station (R) and three base stations (B1, B2, B3) in an exemplary network according to exemplary embodiments of the present invention.

FIG. 2 is a top-plan schematic drawing the rover station (R) and three base stations (B1, B2, B3) in the exemplary network shown in FIG. 1 according to the present invention.

FIG. 3 is a perspective view of the ionosphere delay differentials to selected exemplary methods according to the present invention.

FIG. 4 is a top-plan schematic view of a road application where a reduced level of interpolation of ionosphere delays maybe used according to the present invention.

FIG. 5 is a schematic diagram of an exemplary rover station according to the present invention.

FIG. 6 is a general flow diagram of embodiments of the present invention.

FIG. 7 is a schematic diagram of an exemplary computer program product according to the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0020] FIG. 1 is a perspective view of a rover station (R) and three base stations (B1, B2, B3) in an exemplary network according exemplary embodiments of the present invention, and FIG. 2 is a top-plan schematic drawing thereof. The present invention pertains to estimating the position of the rover station with information provided from two or three of the base stations and with satellite measurements made by the rover station. Referring to FIG. 1, each station has a receiver that receives the satellite positioning signals with a satellite antenna (shown as a substantially flat disk). A plurality of satellites S1-S4 are depicted in FIG.1, with the range between each satellite and each antenna being depicted by a respective dashed line. In the example shown and FIG. 1, the Rover station is operated by a human user, and has a positioning pole for positioning the Rover's satellite antenna over a location whose coordinates are to be determined. The Rover's satellite antenna is coupled to the receiver's processor, which may be disposed in the backpack and carried by the user. The user interacts with the receiver's processor through a keypad/display. The receiver also has a radio modem (more formally a demodulator) that can receive data from the base stations through a conventional RF antenna and relay it to the processor. In other embodiments, the Rover's satellite antenna may be mounted to a vehicle, and the receiver may operate independently and automatically without the need of a human operator. The present invention is applicable to these and other physical embodiments.

[0021] The satellite signals comprise carrier signals which are modulated by pseudo-random binary codes, which are then used to measure the delay relative to local reference clock or oscillator. These measurements enable one to determine the so-called pseudo-ranges between the receiver and the satellites. The pseudo-ranges are different from true ranges (distances) between the receiver and the satellites due to variations in the time scales of the satellites and receiver and various noise sources. To produce these time scales, each satellite has its own on-board atomic clock, and the receiver has its own on-board clock, which usually comprises a quartz crystal. If the number of satellites is large enough (four or more), then the measured pseudo-ranges can be processed to determine the user location (e.g., X, Y, and Z coordinates) and to reconcile the variations in the time scales. Finding the user location by this process is often referred to as solving a navigational problem or task.

[0022] More specifically, the GPS system employs a constellation of satellites in orbit around the earth at an altitude of approximately 26,000 km. Each GPS satellite transmits microwave radio signals in two frequency bands located around 1575.42 MHz and 1227.6 MHz, referred to as L1 band and L2 band, respectively. The GPS L1-band signal is modulated by a coarse/acquisition code (C/A) and a precision ranging code (P-code). The L2-band signal is binary modulated by the P-code. The GPS C/A code is a pseudo-random (PR) Gold code that is specific to each satellite and is used to identify the source of a received signal. The P-code is a pseudo-random code signals and is also specific to each satellite, having a symbol rate which is ten time more than C/A, which reduces the granularity by a factor of ten. The GPS satellite transmission standards are set in detail by the ICD-GPS-200, Revision C, ARINC Research Corporation, 10 October, 1993.

[0023] The satellites of the GLONASS system transmit signals in two frequency bands around 1602 MHz, and around 1246 MHZ, referred to also as L1 band and L2 band, respectively. The GLONASS L1-band signal is modulated by a pseudo-random C/A code and a pseudo-random P-code. The L2-band signal is modulated by the P-code. Unlike GPS, in which all of the satellites transmit on the same nominal frequency, the GLONASS satellites each transmit at a unique frequency in order to differentiate between the satellites. The GLONASS L1-band carrier frequency is equal to 1602 MHz + l*0.5625 MHz, where l is an integer index ranging between 0 and 24 that identifies the satellites. The GLONASS L2-band carrier frequency is equal to 1246 MHz + l*0.4375 MHz. Details of the GLONASS signals maybe found in GLONASS ICD, Version 4.0, 1998.

[0024] The distance between a receiver and a satellite (called the "receiver-to-satellite range") is determined by measuring the time that it takes for the signal to pass from the satellite to the receiver, provided that the position of the satellite is known. The satellites and receivers have internal clocks that are synchronized to a single GPS time. For each satellite signal being tracked, the receiver generates a local version of the satellite's expected PR-code, and then retards that version in time until the local version correlates (i.e., matches) with the received satellite signal. Thereafter, the satellite signal is tracked by advancing or retarding the local version of the PR-code. The carrier phase of the satellite can also be tracked, which is usually done by tracking the Doppler shift of the satellite signal. The positions of the satellites are, except for minor variations, highly predictable as a function of time, and the receiver generally carriers a model of the satellite's position as a function of GPS time. In theory, by determining the ranges to three different satellites, the receiver can perform a three-dimensional triangulation to find its position. But because limitations in the accuracy of the receiver's clock, the internally generated time is offset somewhat from true GPS time. Thus, the ranges to at least four different satellites are simultaneously measured in order to be able to solve for four unknowns, namely the three coordinates of the position of the receiver location (e.g., x, y, and z) and an offset of the receiver clock time from the GPS time. The location is usually performed with respect the defined Cartesian coordinates frame.

[0025] In theory, a GPS receiver can track both the C/A code and the P-code of a satellite. The C/A code generally provides accuracy to within 20 - 50 meters, and the P-code generally provides greater accuracy to within 10 meters because of its higher repetition rate (less granularity) relative to the C/A code. However, knowledge of the P-code is restricted to military users and not available to civilian users. Nonetheless, some approaches for tracking P-codes have been developed.

[0026] The desire to guarantee the solution of navigational tasks with accuracy better than 10 meters, and the desire to raise the stability and reliability of measurements, have led to the development of the mode of "differential navigation ranging," also called "differential navigation" (DN). In the DN mode, the task of finding the user position is performed relative to a Base station (Base), the coordinates of which are known with the high accuracy and precision. The Base station has a navigation receiver that receives the signals of the satellites and processes them to generate measurements. The results of these measurements enable one to calculate corrections, which are then transmitted to a roving GPS receiver, which the user has set up. We call this GPS receiver the "Rover station," or "Rover receiver." By using these corrections, the roving GPS receiver gains the ability to compensate for the major part of the strongly correlated errors in the measured pseudo-ranges, and to substantially improve the accuracy of the estimate of its position.

[0027] Usually, the Base station is immobile during measurements. The rover station may be either immobile or mobile. Depending on the navigational tasks to be solved, different modes of operation may be used in the DN mode. They differ in the way in which the measurement results are transmitted from the Base to the Rover. In the post-processing (PP) mode, these results are transmitted as digital recordings and go to the user after all the measurements have been finished. In the PP mode, the user reconstructs his or her location for definite moments in the past.

[0028] Another mode is the Real-Time Processing (RTP) mode, and it provides for the positioning of the Rover receiver just during the measurements. The RTP mode uses a communication link (such as the radio communication links shown in FIG. 1), through which all the necessary information is transmitted from the Base to the Rover receiver in digital form.

[0029] Further improvement of accuracy of differential navigation may be reached by supplementing the measurements of the pseudoranges with the measurements of the phases of the satellite carrier signals. If one measures the carrier phase of the signal received from a satellite in the Base receiver and compares it with the carrier phase of the same satellite measured in the Rover receiver, one can obtain measurement accuracy to within several percent of the carrier's wavelength, i.e., to within several centimeters.

[0030] The practical implementation of those advantages, which might be guaranteed by the measurement of the carrier phases, runs into the problem of there being ambiguities in the phase measurements.

[0031] The ambiguities are caused by two factors. First, the difference of distances ΔD from any satellite to the Base and Rover is usually much greater than the carrier's wavelength λ. Therefore, the difference in the phase delays of a carrier signal Δϕ=ΔD/λ received by the Base and Rover receivers may substantially exceed one cycle. Second, it is not possible to measure the integer number of cycles in Δϕ from the incoming satellite signals; one can only measure the fractional part of Δϕ. Therefore, it is necessary to determine the integer part of Δϕ, which is called the "ambiguity". More precisely, we need to determine the set of all such integer parts for all the satellites being tracked, one integer part for each satellite. One has to determine this set along with other unknown values, which include the Rover's coordinates and the variations in the time scales.

[0032] In a general way, the task of generating highly-accurate navigation measurements may be formulated by defining a set of unknowns and system of relationships between the unknowns and measured navigation parameters. The vector of unknowns, denoted herein as n_Σ, include three Rover coordinates (usually along Cartesian axes X, Y, Z) in a given coordinate system (sometimes time derivatives of coordinates are added too); the variations of the time scales which is caused by the phase drift of the local main reference oscillator; and n integer unknown values associated with the ambiguities of the phase measurements of the carrier frequencies. The value of n is determined by the number of different carrier signals being processed, and accordingly coincides with the number of satellite channels actively functioning in the receiver. At least one satellite channel is used for each satellite whose broadcast signals are being received and processed by the receiver. Some satellites broadcast more than one code-modulated carrier signal, such as a GPS satellite, which broadcasts a carrier in the L₁ frequency band and a carrier in the L₂ frequency band. If the receiver processes the carrier signals in both of the L₁ and L₂ bands, the number of satellite channels (n) increases correspondingly.

[0033] Two sets of navigation parameters are measured by the Base and Rover receivers, respectively, and are used to determine the set of unknowns, which is sometimes called the "state vector." Each set of navigation parameters includes the pseudo-range of each satellite to the receiver, and the full (complete) phase of each satellite carrier signal. Each pseudo-range is obtained by measuring the time delay of a code modulation signal of the corresponding satellite (C/A code or P-code). The code modulation signal is tracked by a delay-lock loop (DLL) circuit in each satellite-tracking channel. The full phase of a satellite's carrier signal is tracked by a phase-lock-loop (PLL) in the corresponding satellite tracking channel. (The DLL and PLL are, for example, provided by the demodulator 120 of an exemplary rover shown in FIG. 5). An observation vector is generated as the collection of the measured navigation parameters for specific (definite) moments of time.

[0034] The relationship between the state vector and the observation vector is defined by a well-known system of navigation equations. Given an observation vector, the system of equations may be solved to find the state vector if the number of equations equals or exceeds the number of unknowns in the state vector. In the latter case, conventional statistical methods are used to solve the system: the least squares method, the method of dynamic Kalman filtering, the method of least squares and various modifications of these methods.

[0035] One method may comprise the following steps. The measured values of the pseudo-ranges and full phases at specific (definite) moments of time, along with an indication of the satellites to which these measurements belong to and the time moments of the measurements, are transmitted from the Base to the Rover (such as through the communication link or as recordings). Corresponding values are measured in the Rover receiver. The processing includes the determination of the single differences of the pseudo-ranges and full phases between the Base and Rover measurements for each satellite. The strongly correlated errors are largely compensated (i.e., substantially cancelled) in the single differences. Then, the residuals of the single differences are calculated by subtraction of calculated values from the measured results. The processing of residuals allows one to linearize the initial system of navigation equations (sometimes several subsequent iterations are necessary for that), which makes possible the use of the well-developed body of mathematics for solving systems of linear equations. The subsequent iterative solution of the linearized system of navigation equations is equivalent to the minimization of the sum of squared non-linear residuals by the Gauss-Newton minimization method. The components of the state vector, with the n ambiguities included, are found as a result of the solution. But the calculated values of the ambiguities are not necessarily integer numbers, and are often floating point numbers. Because of this, they are called "float ambiguities," or "floating ambiguities," at this stage of the solution. To find true values of the integer ambiguities one uses the procedure of rounding off the float ambiguity vector to the nearest set of integers. This process is called 'the ambiguity resolution'. After the ambiguity resolution has been done, is it possible to generate more accurate values of residuals and then, by solving the system of equation again, to find the coordinate values for the baseline connecting the Base and Rover, and consequently to more accurately estimate the coordinates of Rover and the correction to its clock drift.

[0036] There are fractional parts associated with each ambiguity due to the time offset in the receiver's carrier generator, and as a practical matter, it is more convenient to include this fractional offset into the floating ambiguities and "integer" ambiguities. In this case, one additionally solves for the unknown fractional offset of the receiver's carrier generator, and then resolves the "integer" ambiguities in the form of integers plus a common fractional part that is related to the time offset of the receiver's carrier generator. We call these resolved ambiguities "fixed-integer ambiguities" because, although these ambiguities have fractional parts, the difference between any two fixed-integer ambiguities for two corresponding satellites measured by the same pair of receivers is an integer.

[0037] Even with all of the-above described processing to account for clock offsets and carrier ambiguities, there are additional factors which affect the accuracy of measurements made with GPS and/or GLONASS signals. As one factor, the trajectory of each satellite (or its initial data called the ephemeris), is elliptical and is affected by natural causes such as solar winds. The accuracy of any measurement is dependent upon knowledge of the position of the satellites at certain time. An estimate of the ephemeris is calculated on earth for each of the satellites and is periodically uploaded to the satellite. The position information of a satellite is encoded onto a low frequency (50 Hz) signal which is modulated on to one of the carrier signals, and transmitted to the GPS receiver on earth.

[0038] Two additional and important factors that affect the accuracy of measurements made with GPS and/or GLONASS signals are the effects of the troposphere and ionosphere on propagation of signals from the satellites to the receivers. The troposphere is the lower part of the atmosphere and variations in the temperature, pressure, and humidity lead to spatial variations in the signal propagation. The ionosphere is at the upper part of the atmosphere and has a slice of ionized gas at the altitude of around 300 km. The density of ionized particles is sufficiently high to affect the propagation of electromagnetic signals, and has a spatial variation and a time variation. The ionosphere effect becomes even more important during years of high solar activity. These variations in the troposphere and ionosphere introduce variable delays in the propagation the satellite signals to the receivers. If the base and rover are widely separated, these delays will be significantly different for the base and rover stations, and will introduce error into the estimation of the rover's position.

[0039] With that general overview, we now describe the invention in greater detail. For the sake of simplifying the presentation, and without loss of generality, we assume "N" satellites identified by the index "s", s = 1, ..., N, and we assume that each receiver can track the satellite's L1 band signal and the satellites L2 band signal. The receivers extract timing information from the satellite signals, and report this information a predefined increments k of time, which we call epochs k. The time between epochs can be selected by the user, and generally ranges between 0.1 seconds to 2 seconds, with 1 second being typical. The clocks of all of the receivers are typically accurate to within several milliseconds of the true GPS time, and for practical purposes the receivers can determined the number k of the current epoch from their clocks. The following timing information can be extracted from each satellite "s" at each epoch "k" by each receiver "r":

1. The low-frequency (50 Hz) information signal which provides information on the orbit (position) of the satellites which enables the receiver to determine the satellite's position.

2. the pseudo-range

derived from the L1-band C/A code (or optionally the L1-band P-code for military users), and having the units of length (e.g., meters [m]);

3. the pseudo-range

derived from the L2-band C/A code (or optionally the L2-band P-code for military users), and having the units of length (e.g., meters [m]);

4. the L1-band carrier phase

derived from the L1-band carrier, and typically having the dimensionless units of cycles (but is sometimes expressed in terms of meters by multiplying the cycles by the L1-band wavelength λ^L1,s; and

5. the L2-band carrier phase

derived from the L2-band carrier, and typically having the dimensionless units of cycles (but is sometimes expressed in terms of meters by multiplying the cycles by the L2-band wavelength λ^L2,s.

Each of

and

are known as observed quantities, or "observables," because the are measured by the receiver from the satellite signals. The observables are related to the speed of light "c," the wavelengths λ^L1,s and λ^L2,s of the L1-band and L2-band carriers of satellite "s," the frequencies f ^L1,s =c/ λ^L1,s and f^L2,s =c/λ^L2,s of the L1-band and L2-band carriers of satellite "s," various variables that are to be determined, and various noise sources, in the following manner:







where variables (which are to be determined) are:

• 
  
  is the true range between the satellite "s" and receiver "r" at the epoch "k", having dimension of distance (usually expressed as meters [m]);
• 
  
  is the time offset from true GPS time of the clock of satellite "s" at epoch "k";
• τ_r,k is the time offset from true GPS time of the clock of receiver "r" at epoch "k";
• 
  
  is the delay due to tropospheric effects between satellite "s" and receiver "r" at epoch "k";
• 
  
  is the delay due to ionospheric effects between satellite "s" and receiver "r" at epoch "k" (the full amount of
  
  affects the pseudo-range in the L1-band);
• 
  
  is the integer phase ambiguity in the L1-band observable
  
  
• 
  
  is the integer phase ambiguity in the L2-band observable
  
  
• 
  
  is the initial phase offset of the L1-band phase tracker of receiver "r"; and
• 
  
  is the initial phase offset of the L2-band phase tracker of receiver "r",

and where various noise sources are:

• 
  
  is the total effect of the noise sources on the pseudo-range measurement at epoch "k" in receiver "r" when tracking the L1-band C/A-code signal (or P-code signal) of satellite "s";
• 
  
  is the total effect of the noise sources on the pseudo-range measurement at epoch "k" in receiver "r" when tracking the L2-band C/A-code signal (or P-code signal) of satellite "s";
• 
  
  is the total effect of the noise sources on the carrier-phase measurement at epoch "k" in receiver "r" when tracking the L1-band carrier of satellite "s"; and
• 
  
  is the total effect of the noise sources on the carrier-phase measurement at epoch "k" in receiver "r" when tracking the L2-band carrier of satellite "s".

Forms [1A]-[1D] are known as the satellite navigation equations.

[0040] In embodiments of the present invention, we will be forming differences between the observables of pairs of stations, and differences between instances of the satellite navigation equations. The vector, or straight line, between a pair of two such stations is called a baseline. The baselines between all of the stations shown in FIG. 1 are best seen in the top plan view of FIG. 2. We generally note the difference of an observable measured by two stations with the prefix notation Δ_q,r, where each of "q" and "r" represents one of the stations B1, B2, B3, and R. For example,







Forms [2A]-[2D] are often referred to as the between-station (or between-receiver) single differences of the signals of satellite "s" between stations (receivers) "r" and "q". The between station operator Δ_q,r can be applied to the variables and noise sources as well. For example,

and

With this background, we can relate the between-station single differences of the observables to the differences in the variables as follows:







The difference form of [3A] is generated by forming two instance of form [1A] for receivers "r" and "q", and then subtracting the two instances (the instance for receiver "q" is subtract from the instance for receiver "r"). Difference forms [3B], [3C], and [3D], are formed in a similar manner from corresponding instances of forms [1B], [1C], and [1D], respectively. Forms [3A]-[3D] are the single-differences of the navigation equations. The benefit of forming the between-station single differences is that the error term representing the time offset of the satellite clock,

is cancelled out in the differences. We emphasize that the forms [3A]-[3D] can be applied to each satellite that can be observed by receivers "q" and "r." Higher-order differences of the navigation equations, such as the double-differences of the navigation equations, can be formed and are known to the art. For example, a common double-difference equation is the difference between two singles-difference equations associated with a common baseline, but with each single-difference equation being based on a different satellite. The present invention may also use these higher-order differences of the navigation equations, although the single differences of the navigation equations are currently preferred. Each of these difference forms is generically referred to as a differential navigation equation.

Between Base Station Processing, Part I.

[0041] Because the locations of the base stations are known, and because the locations of the satellites as a function of epoch time (k) are also known, the between station differences of each true range

associated with each satellite "s" can be generated from existing information. If vectors X_r, X_q, and X^s represent the locations of receiver "r", receiver "q", and satellite "s", respectively, in a coordinate system (e.g., Cartesian coordinate system), and the operator ∥·∥ represent the distance operator in that coordinate system, then

This reduces by one the number of unknowns in forms [3A]-[3D]. In addition, the Goad-Goodman model may be used to model the difference in troposphere effects (with an error less than a few percent), and thus the difference

may be estimated based on the positions of the receivers and the satellite (more specifically, the angles between the receivers and satellites). The noise sources Δ_q,rn^L1,s, Δ_q,rn^L2,s, Δ_q,rv^L1,s, and Δ_q,rv^L2,s can never be known, but they are generally zero-mean and their effect can be reduced by averaging. Thus, the number of solvable unknowns in forms [3A]-[3D] may be reduced to the following six: (1) Δ_q,rτ_k, (2)

(3) Δ_q,rN^L1,s, (4) Δ_q,_rψ^L1, (5) Δ_q,rN^L2,s (6) Δ_q,rψ^L2. The first unknown varies with time and is common to all of the satellites being tracked by receivers "q" and "r." The second unknown varies with time and is specific to the satellite "s" being tracked by the pair of receivers "q" and "r." The third and fifth unknowns are each specific to the satellite "s" being tracked by the pair of receivers "q" and "r", and each does not normally vary with time unless a cycle slip occurs in the receivers phase-lock loop. The forth and sixth unknowns are specific to the pair of receivers "q" and "r," and do not normally vary with time.

[0042] As a practical matter, we note that the third and fourth unknowns are related to the L1-carrier phase measurement of satellite "s" and are time-independent (unless a cycle slip occurs). In theory, these unknowns can be represented as a combined unknown Δ_q,rN̂^L1,s = Δ_q,rN^L1,s + Δ_q,rψ^L1, which we call the between-station "fixed-integer ambiguity" for the L1 carrier of satellite "s," as measured at stations "q" and "r." We call these resolved ambiguities "fixed-integer ambiguities" because, although these ambiguities have fractional parts, the difference between any two fixed-integer ambiguities for two corresponding satellites measured by the same pair of receivers is an integer. In a similar manner, the fifth and sixth unknowns are related to the L2-carrier phase measurement of satellite "s" and are time-independent (unless a cycle slip occurs); they can be represented as a combined unknown Δ_q,rN̂^L2,s = Δ_q,rN^L2,s + Δ_q,rψ^L2, which we call the between-station "fixed-integer ambiguity" for the L2 carrier of satellite "s", as measured at stations "q" and "r"

[0043] As a further practical matter, one first generates floating point versions of the fixed-integer ambiguities, and then applies a discretization process to the floating point version to generate the fixed-integer ambiguities. We call these versions the floating-point ambiguities, and denote them as Δ_q,rN^L1,s ≅ Δ_q,rN^L1,s + Δ_q,rψ^L1 and Δ_q,rN^L2,s ≅ Δ_q,rN^L2,s + Δ_q,rψ^L2.

[0044] Thus, the solvable unknowns for each instance of form [3A]-[3D] can be reduced to four: (1) Δ_q,rτ_k, (2)

(3) Δ_q,rN̂^L1,s(Δ_q,rN^L1,s), and (4) Δ_q,rN̂^L2,s (Δ_q,rN^L2,s). The first unknown is common to all the satellites being tracked by the pair of receivers "q" and "r," whereas the last three are specific to the satellite "s." The first two unknowns vary with time, whereas the last two are time invariant (unless a cycle slip occurs). For the base stations, the known values of forms [3A] - [3D] can be represented as:







Forms [4A]-[4D] comprise the known terms of the single-differences of the navigation equations, and we call them the "residuals" of the single differences, or more generally the "residuals of a set of differential navigation equations". The magnitude of each residual is generally less than the magnitudes of one or more of the known terms that forms the residual.

[0045] Then, the unknowns can be estimated from the residuals using the following forms by any of number of solution methods known to the art:

[0046] All of the residuals, forms, known values, and unknown variables are real-valued. The estimation process usually includes instances of forms [5A]-[5D] for several satellites, and for several epochs of time.

[0047] As one aspect of the present invention, one or more of the unknown variables for several satellites are estimated for at least two base stations, and preferably for at least three base stations by a process that is performed at the rover. Using the numbers 1, 2, and 3 to represent the base stations B1, B2, and B3, respectively, in the difference operator "Δ_q,r", the estimated values of the between-base station unknowns for each satellite "s" at each epoch "k" are:





An exemplary estimation process is outlined in a section below entitled "Between Base Station Processing, Part II." As one option, the estimation process may break down the fixed integer ambiguities into their components as follows:





In some applications of the present invention where lower estimate accuracy is acceptable, floating-point ambiguities may be used in place of the fixed-integer ambiguities, and the following set of between-base station unknowns may be generated:

Between Rover and Base Station Processing.

[0048] The processing of differences between the rover station and any one of the base stations is more complex because we do not know the position of the rover beforehand.

[0049] Thus, the term

is not exactly known. However, given an initial estimated value of the rover's location, which we will denote as X₀ and which can be generated from the 50 Hz information signals by means known to the art, we can generate an initial range estimate between satellite "s" and the rover, which we denote as

and we can generate a linearized approximation of the term as follows, where we use r=0 to denote the rover and use q to generally indicate any one of the base stations:

where δX_k is the vector difference between the actual location X₀ of the Rover and the initial estimated location X₀ (X₀ = X₀ + δX_k), where

is a row vector comprised of the partial derivatives of the distance form

with respect to the rover location X₀, as evaluated at X₀, and where

has been used as a shorthand notation for

Formally, row vector

is expressed as:

The values of

depend upon the satellite location, which changes with each time moment "k," and upon the initial location X₀ of the Rover, which may be periodically updated, particularly if the Rover is moving. The row vectors

for all of the satellites may be collected together as a single s-by-3 matrix, which we denote as A_k. Matrix A_k is commonly known as the Jacobian matrix, the geometry matrix, and the matrix of directional cosines. It is commonly computed in the art and described in many tutorial textbooks on global positioning. The reader unfamiliar with the GPS is directed to these tutorial texts for more detailed explanations of how matrix A_k (which is oftentimes referred to matrix H or matrix G by these texts) is generated.

[0050] With

we may write the following versions of forms [4] (residuals) for the baselines between the Rover ("0") and any one of the base stations ("q"):







and the following versions of forms [5]

[0051] The solvable unknowns for form [9] includes δX_k, as well as Δ_q,0τ_k,

Δ_q,0N̂^L1,s, and Δ_q,0N̂^L2,s. As described below in greater detail, estimation processes for these unknowns generally include instances of forms [9A]-[9D] for several satellites, and for several epochs of time.

[0052] While the presentation of this section has been made with respect to a specific rover station (0), it may be appreciated that the discussion and above forms generally apply to any pair of receivers (q, r), where "r" substitutes for "0" in the above.

Development of the Present Invention

[0053] As part of making their invention, the inventors have recognized that the base station time-offset unknowns, when accurately estimated, should satisfy the following relationship:

An underlying meaning of this relationship can be seen by noting that Δ_3,1τ_k = -Δ_1,3τ_k, and by rewriting the relationship in the equivalent form of Δ_2,1τ_k + Δ_3,2τ_k + Δ_1,3τ_k = 0. That is, the sum of the time offsets around a loop of base stations is equal to zero. The other unknowns, when accurately estimated, should satisfy the following similar relationships:

















As a further part of making their invention, the inventors have recognized that the above relationships [10A]-[10J] should be satisfied by any set of three receivers, including sets where one of the receivers is the receiver of the rover station. We illustrate this point by replacing station B3 (3) with the rover station, which we will identify by the subscript number "0":



















Still further, the inventors have recognized that relationships [10] and [11] can be generalized to apply to any loop of four or more receivers. Nonetheless, we provide exemplary embodiments of the present invention using loops of three receivers in order to simplify the presentation of the invention.

[0054] According to general aspects of the present invention, the position of the Rover is estimated by forming a primary baseline between the Rover and one of the base stations, usually the closest base station, and then forming one or more secondary baselines from the Rover to other base stations. Then, one or more of the above relationships are applied to the configuration of stations to relate the measured data associated with the secondary baseline(s) with the measured data associated primary baseline using one or more of the unknowns associated with the baselines between base stations through forms [11]. To simplify the presentation of the present invention, and without loss of generality, we will use base station B1 to form the primary baseline with the Rover, and we use base stations B2 and B3 to form the secondary baselines with the Rover. Varying amounts measured data from the secondary baselines may be related with the primary baseline. In general, the greater amount of information so related increases the accuracy of the estimated position of the rover, and/or enables a greater spacing between base stations.

First General Group of Embodiments

[0055] In a first exemplary embodiment, the measured pseudo-range data from the secondary baselines are related with the measured pseudo-range data of the primary baseline. At first, only the L1-band data is used (forms [4A], [5A], [8A], and [9A]). We take the case where the distances between the stations are small enough that the difference terms associated with the ionosphere terms

are negligible. For the primary baseline, forms [8A] and [9A] reduce to:



For the secondary baseline to the second base station, we have:



For the secondary baseline to the third base station, we have:



The terms in forms [12A], [14A], and [16A] are the residuals of differential navigation equations and are known. The unknowns are contained in right-hand sides of forms [13A], [15A], and [17A]. There are a total of six solvable unknowns: Δ_1,0τ_k, Δ_2,0τ_k, Δ_3,0τ_k, and the three components of δX_k. However, using form [11A], Δ_2,0τ_k may be related to Δ_0,1τ_k through the estimated base-station time offset Δ_2,1τ_k as follows: Δ_2,0τ_k = Δ_2,1τ_k-Δ_0,1τ_k=Δ_2,1τ_k+Δ_1,0τ_k. In a similar manner, Δ_3,0τ_k may be related to Δ_0,1τ_k through the estimated base-station time offset Δ_3,1τ_k as follows: Δ_3,0τ_k = Δ_3,1τ_k-Δ_0,1τ_k = Δ_3,1τ_k+Δ_1,0τ_k. These two forms reduce the number of true solvable unknowns to four, and the following modified set of forms may be used to estimate the true solvable unknowns:





As an equivalent, one may view forms Δ_2,0τ_k = Δ_2,1τ_k + Δ_1,0τ_k and Δ_3,0τ_k = Δ_3,1τ_k + Δ_1,0τ_k as increasing the total number of forms by two, and may then estimate the six unknowns the expanded form set:









The rover's location (X₀ = X₀ + δX_k) may be estimated from each of the above form sets using any one of several know methods. Here, we demonstrate estimating the rover's location with a least squares fitting approach based on the first form set. After generating the residuals

for N satellites (s=1 to s=N) for the baseline between the rover and the first base station (R-B1), we collect them together into a first vector:

We do the same for the other two baselines, but modify their residuals according to the between-base station time offsets cΔ_2,1τ_k and cΔ_3,1τ_k :



where the superscript" "*" is used to indicate the modification. The noise terms can be similarly grouped as:



and

The first form set of [13A], [15A*] and [17A*] may then be written in matrix form as:

The solvable unknowns

may be estimated by a least squares process as follows:

where:

and where C_n,k is a 3N-by-3N covariance matrix for the noise terms



and

The generation of covariance matrix C_n,k is well known to the GPS art and described in the technical and patent literature (see for example U.S. patent No. 6,268,824, where the covariance matrices are denoted as matrices R), and a description thereof is not needed for one of ordinary skill in the GPS art to make and use the present invention. (In a subsequent section, we describe an estimation process that we prefer to use, and which may be applied to these embodiments.)

[0056] For the reader not familiar with the GPS art, we briefly note that matrix C_n,k generally comprises a diagonal matrix, with each diagonal element being related to the noise sources in the two receivers that define the baseline (in this case the rover and one of the base stations). A covariance factor is usually associated with each satellite signal received by each receiver, and this covariance factor is usually related to the signal-to-noise ratio of the signal (as received by the receiver) and the elevation angle of the satellite (the multipath error has a strong correlation with the elevation angle). Each diagonal entry of matrix C_n,k usually comprises an addition of the two covariance factors associated with the two receivers which contributed to the underlying noise quantity, e.g., base station B1 and the rover for noise quantity

For more details and information on the generation of the covariance matrices, the reader is direct to A. Leick, GPS Satellite Surveying, John Wiley & Sons, (1995). Matrix

is known as the observation matrix, and it relates the solvable unknowns to the residuals. The solvable unknowns may also be estimated by other processes, such as various Kalman filtering processes.

[0057] The above may be carried out by omitting the rows related to one of the secondary base stations B2 and B3, such as the last N rows associated with the third base station. The above may also be carried out by adding rows related to a fourth base station (and even more base stations).

[0058] The second form set comprising [13A], [15A], [17A], [11A*], and [11A**] may be written as:

and the solvable unknowns may similarly be estimated by various least squares processes, and Kalman filtering processes. The observation matrix in the above form is denoted as

[0059] Thus, the above exemplary embodiments provide methods of estimating the location of the rover station (R) with the use of a first base station (B1) a second base station (B2), and optionally a third base station (B3) or more base stations. In summary, the locations of the base stations were obtained, and one of the base stations (e.g., B1) was selected to form a primary baseline with the Rover station. We refer to this base station as the primary base station, and the other base stations as the secondary base stations. Additionally, for each of the secondary base stations, the time offset representative of the time difference between the clocks of the primary station and secondary base station is obtained. Also, measured satellite data as received by the rover, the primary base station, and the secondary base station(s) is obtained. From this, the set of residuals

associated with the primary baseline (R-B1) is generated, and is related to the measured satellite data received by the rover station and the first base station, the locations of the satellites, and the locations of the rover station and the first base station. Similarly, the set(s) of residuals



etc. associated with the secondary baseline(s) are generated, each set of residuals related to the measured satellite data received by the rover station and the secondary base station, the locations of the satellites, and the locations of the rover station and the secondary base station. Thereafter, the rover's location is estimated from the above sets of residuals, the time offset between the clocks of the base stations, and typically an observation matrix.

[0060] The above embodiments can be equally implemented using the L2-band signals. The forms for the primary baseline (neglecting ionosphere terms) are:



For the secondary baseline to the second base station, we have:



For the secondary baseline to the third base station, we have:



Not only may these forms be used in place of forms [12A]-[17B], but they may be used in addition to forms [12A]-[17B]. In the latter case, the first form set [18] expands to

where:



From form [18+], the solvable unknowns may be estimated by a least squares process.

[0061] One might envision a different approach whereby the Rover's position is estimated by using each of the three baselines separately to generate three separate estimates of the Rover's location, and then averaging the three separate estimates to generate a final estimate. However, the present invention provides more accurate results than this possible approach because the present invention uses the additional information provided by forms [11] (specifically, [11A], [11A*] and [11A**]), which correlates the values of the unknowns associated with the baselines. The achievement of more accurate results by the present invention is also true for the embodiments described below.

Second General Group of Embodiments

[0062] The second group of embodiments builds upon the first group of embodiments by generating and utilizing the residuals derived from the phase measurements at the receivers. We take the case where the distances between the stations are small enough that the difference terms associated with the ionosphere terms

are negligible. In later embodiments, we will take these ionosphere terms into account. With this assumption, forms [8C], [9C], [8D], and [9D] for the primary baseline become the following forms [12C], [13C], [12D], and [13D], respectively:







For the secondary baseline to the second base station, we have:







For the secondary baseline to the third base station, we have:







The terms in forms [12C, D], [14C, D], and [16C, D] are the residuals of the differential navigation equations and are known. The unknowns are contained on the right-hand sides of forms [13C, D], [15C, D], and [17C, D]. For N satellites, there are 6*N equations and a total of (6+ 6*N) solvable unknowns: Δ_1,0τ_k, Δ_2,0τ_k Δ_3,0τ_k, the three components of δX_k, and N instances of each of Δ_1,0N̂^L1,s, Δ_2,0N̂^L1,s, Δ_3,0N̂^L1,s, Δ_1,0N̂^L2,s, Δ_2,0N̂^L2,s, and Δ_3,0N̂^L2,s, for s = 1 to s = N satellites. However, using forms [11A], [11C], and [11D], the number of unknowns may be reduced to 4+2*N. As we saw above, Δ_2,0τ_k, may be related to Δ_0,1τ_k through the estimated base-station time offset Δ_2,1τ_k using form [11A] as follows: Δ_2,0τ_k = Δ_2,1τ_k - Δ_0,1τ_k = Δ_2,1τ_k + Δ_1,0τ_k. In a similar manner, Δ_3,0τ_k was related to Δ_0,1τ_k through the estimated base-station time offset Δ_3,1τ_k as follows: Δ_3,0τ_k = Δ_3,1τ_k - Δ_0,1τ_k = Δ_3,1τ_k + Δ_1,0τ_k. Form [11C] may be used to related each of the L1 band ambiguities of the secondary baselines to the primary baseline as follows:



Similarly, Form [11D] may be used to relate each of the L2 band ambiguities of the secondary baselines to the primary baseline as follows:



Forms [15C] and [15D] for the second base station B2 may then be modified as follows:



Forms [17C] and [17D] for the third base station B3 may be similarly modified:



Similar to form [18⁺], forms [13C, D] and modified forms [15C*, D*] and [17C*, D*] can be written in matrix form:

where:

• 
  
  is an N x1 column vector of the L1-band phase residuals
  
  associated with the primary baseline,
• 
  
  is an N x 1 column vector of the modified L1-band phase residuals
  
  associated with the secondary baseline between the rover and base station B2,
• 
  
  is an N x 1 column vector of the modified L1-band phase residuals
  
  associated with the secondary baseline between the rover and base station B3,
• 
  
  is an N x 1 column vector of the L2-band phase residuals
  
  associated with the primary baseline,
• 
  
  is an N x 1 column vector of the modified L2-band phase residuals
  
  associated with the secondary baseline between the rover and base station B2,
• 
  
  is an N x 1 column vector of the modified L2-band phase residuals
  
  associated with the secondary baseline between the rover and base station B3,
• A_k is the derivative matrix previously described,
• Λ_L1 is a diagonal matrix of the carrier wavelengths of the satellites in the L1-band, and
  
  is its inverse matrix,
• Λ_L2 is a diagonal matrix of the carrier wavelengths of the satellites in the L2-band, and
  
  is its inverse matrix,
• f^L1 is a column vector of the carrier frequencies of the satellites in the L1-band, where
  
  where c is the speed of light and 1 is a column vector of 1's,
• f^L2 is a column vector of the carrier frequencies of the satellites in the L2-band, where
  
  
• I_NxN is an N x N identity matrix, and
• 0_NxN is an N x N matrix of zeros.

The solvable unknowns [δX_k, Δ_1,0τ_k, Δ_1,0N̂^L1, Δ_2,0N̂^L2]^T may be estimated by applying a number of processes to the combination of forms [21] and [18+]. Further below, in a subsequent section, we described a preferred process that can be used on the combination of forms [21] and [18+]. Here, we describe how a least squares process maybe applied to combined forms of [18+] and [21].

[0063] To combine form [21] with [18+], we rewrite form [22] to substitute c·Δ_1,0τ_k for Δ_1,0τ_k as one of the unknowns, using the facts that

and



This facilitates the combination of forms [18+] and [22] as:

A least squares process is applied to form [23] to generate the floating ambiguities over several epochs, and the floating ambiguities are averaged to generate a estimate of the floating ambiguities. For each epoch, the following may be generated:

where

is the observation matrix of form [23] (the matrix which is multiplying the solvable unknowns in form [23]), and where different covariance matrixes

and

are used for the L1-band and L2-band data since the magnitudes and variances of the noise sources associated with the phase measurements are different from those of the noise sources associated with the pseudorange measurements. Also, the least squares method normally produces the floating ambiguities Δ_1,0N^L1, Δ_1,0N^L2 rather than the fixed-integer ambiguities Δ_1,0N̂^L1, Δ_1,0N̂^L2. In practice, the least squares process is applied over many epochs, and the computed floating ambiguities are averaged to generate a final estimate of the floating ambiguities. Several averaging processes are described in U.S. patent No. 6,268,82, and may be used. After generating a suitable set of floating ambiguities, a conventional method of generating the fixed-integer ambiguities or the integer ambiguities may take place.

[0064] With the fixed-integer ambiguities estimated, the unknowns δX_k and c·Δ_1,0τ_k may be estimated by substituting the estimated values of Δ_1,0N̂^L1 and Δ_1,0N̂^L2 into form [23], and moving these terms to the left-hand side with the residuals to provide form [24]:

We consider the left-hand side of form [24] to be a plurality of sets of residuals since each comprises the known quantities of differential navigation equations. A second least squares process may then be applied based on form [24] to estimate the unknowns δX_k and c·Δ_1,0τ_k as follows:



where

is the observation matrix of form [24] (the matrix which is multiplying the solvable unknowns in form [24]). In form [25], the floating ambiguities may be used in place of the fixed-integer ambiguities. However, lower accuracy generally results, although the estimation speed is increased since the step of generating the fix-integer ambiguities from the floating ambiguities may be omitted.

[0065] With large amount of measurement data afforded by the present invention, various residuals may be omitted from use in the estimation process. For example, we may only work with L1-band data of all three stations and only use the residuals associated with this data. We may also only work with data and residuals from two base stations (the primary baseline and one secondary baseline). For applications needing lower accuracy, we may work with the phase and pseudorange data of the primary baseline (R-B1) and just the pseudorange data or phase data of one of the secondary baselines. Also, one can undertake an analysis of the satellite constellation and select the satellites which should provide the highest accuracy, using the pseudo-range and phase data from the L1- and L2- bands. Finally, while we have illustrated the invention with the single-difference navigation equations, it may be appreciated that higher-order differences of the navigation equations may be used. Such higher-order differences have known quantities (which form the residuals) and similar unknowns to be solved for, which can be solved by the above-described methods.

[0066] Thus, the above exemplary embodiments from the second group of embodiments provide methods of estimating the location of the rover station (R) with the use of a first base station (B1) a second base station (B2), and optionally a third base station (B3) or more base stations. As a summary of an exemplary embodiment of the second group, the locations of the base stations were obtained, and one of the base stations (e.g., B1) was selected to form a primary baseline with the Rover station. Additionally, for each of the secondary base stations, the time offset representative of the time difference between the clocks of the primary and secondary base stations is obtained, and a set of satellite-phase cycle ambiguities related to the baseline between the secondary and primary base stations is obtained for both of the frequency bands. Also, measured satellite data as received by the rover, the primary base station, and the secondary base station(s) is obtained. From this, the sets of residuals





and

of differential navigation equations associated with the primary baseline (R-B1) are generated, and are related to the measured satellite data received by the rover station and the first base station, the locations of the satellites, and the locations of the rover station and the first base station. Similar set(s) of residuals associated with the secondary baseline(s) are generated, each set of residuals related to the measured satellite data received by the rover station and the secondary base station, the locations of the satellites, and the locations of the rover station and the secondary base station. Thereafter, the rover's location is estimated from the above sets of residuals, the time offset between the clocks of the base stations, the sets of satellite-phase cycle ambiguities related to the baseline between the primary base station and the secondary base stations, and typically an observation matrix.

Third Group of Embodiments

[0067] In the above embodiments, the ionosphere delays were assumed to equally affect the rover and base stations, and the between-station differences were neglected. When the base stations and rover are separated by large distances, better accuracy may be obtained by taking into account the ionosphere delays. This can be done in a number of ways according to the present invention. FIG. 3 provides a representation of the ionosphere delays of one satellite "s" at the base and rover stations. Shown is a 3-d Cartesian system having two planar axes, north (n) and east (e), to represent the terrain on which the stations are located, and a vertical axis to represent the ionosphere delays of a satellite "s" as a function of the terrain. The ionosphere delay will be different for each satellite. The locations of the rover station R and three base stations B1, B2, and B3 are indicated in the north-east plane of the figure. The ionosphere delays for each of these stations are indicated as





and

respectively. The preferred embodiments of the processing of the base station data, which is more fully described below, generates estimates for the between base stations differences in the ionosphere delays



and

which we call ionosphere delay differentials. From two of these differentials, an estimate for the ionosphere delay between the rover and any of the base stations can be generated. Here, we are most interested in the difference

associated with the primary baseline, the one between the rover and the first base station.

[0068] The first approach is to generate an estimate

of

based on an interpolation of two of the known ionosphere delay differentials (





) onto the known approximate location of the rover. Here, we use

and

in the following interpolation:

where α and β are interpolation constants. The interpolation constants are determined as follows. Let X₁, X₂, and X₃ be three-dimensional vectors which represent the positions of base stations B1, B2, and B3, respectively. Let X_0,k represent the approximate estimated position of the rover at the "k" epoch. Furthermore, let the notation {X}_n denote the north component of a position vector X or a difference vector X of positions, and the notation {X}_e denote the east component of a position vector X or a difference vector of positions X. We can then write the north and east components of the position differences {X_0,k-X₁}_n and {X_0,k-X₁}_e as:

There are two equations in the two unknowns α and β, which can be readily solved for α and β. When X_0,k is within the triangle formed by the base stations, both of α and β are greater than zero, and their sum is equal or less than one.

[0069] Because X_0,k is not necessarily at the exact position of the rover, the estimate

will not necessarily be equal to the true value

In addition, the ionosphere delay does not always vary in a linear manner over the terrain, and often has second order variations with respect to the east and north directions, which are not modeled well by forms [26] and [27]. We model the difference between

and

caused by these effects by the unknown quantity

and thus we can write:

We can also relate

to

as follows:

which is graphically shown in FIG. 3.

[0070] With form [28], estimates for ionosphere differentials on the secondary baselines

and

can be generated using form [11B]

as follows:

[0071] In composing forms [12] - [17], we neglected the ionosphere delays. In the third group of embodiments, we add the ionosphere delay terms to these forms. By comparing the general forms [9A-D] to the specific forms [13A-D], [15A-D], and [17A-D], we can generate augmented forms [12]-[17] as follows:
The primary baseline -















The secondary baseline to the second base station B2-















The secondary baseline to the third base station B3-















This set of forms comprises N additional solvable unknowns, as present in the vector δ_1,0I_k, which have been incorporated into forms [13'], [15'], and [17']. Also, the rough ionosphere approximation Δ_1,0Ĩ_k has been incorporated into forms [12'], [14], and [16']. Finally, the between-base-station data Δ_2,1I_k has been incorporated into forms [14'], and the between-base-station data Δ_3,1I_k has been incorporated into forms [16'].

[0072] The above-described processes of estimating the floating ambiguities and thereafter estimating the rover position can be expanded to include the unknowns δ_1,0I_k. For lower accuracy, the unknowns δ_1,0I_k may be omitted from the above forms [13'], [15'], and [17']. However, approximate information on the ionosphere delays is incorporated into forms [12'], [14'], and [16'].

Embodiment Implementations

[0073] Having thus described three general groups of embodiments, we now describe an exemplary rover station 100 in FIG. 5 that may be used to implement any of the above-described embodiments. Description of rover station 100 is provided in conjunction with a flow diagram shown in FIG. 6. Referring to FIG. 5, rover 100 comprises a GPS antenna 101 for receiving navigation satellite signals, and RF antenna 102 for receiving information from the base stations, a main processor 110, an instruction memory 112 and data memory 114 for processor 110, and a keyboard/display 115 for interfacing with a human user. Memories 112 and 114 may be separate, or difference sections of the same memory bank. Rover 100 further comprises a satellite-signal demodulator 120 for generating the navigation data





and

for each epoch k from the signals received by GPS antenna 101, which is provided to processor 110. Rover 100 also comprises a base-station information demodulator 130 that receives information signals from the base stations by way of RF antenna 102. Demodulators 120 and 130 may be of any conventional design. The information received by demodulator 130 includes the positions (X₁, X₂, X₃) of the base stations, the satellite-navigational data (e.g., k,





and

r =1,2,3) received by each base station at each epoch k, and the between-base station unknowns (e.g., Δ_r,q,τ_k, Δ_r,qN^L1,s, Δ_r,qψ^L1, etc., {r,q} = {1,2},{2,3},{3,1},). Each set of information maybe transmitted on a respective frequency channel. The between-base station unknowns may be generated by the first base station B1, and thereafter transmitted to the rover by the first base station. The first base station may receive the satellite-navigation data from the other base stations in order to compute the between-base station unknowns. Methods of generating the between-base station unknowns are described below in greater detail in the section entitled Between Base Station Processing, Part II. As another approach, the between the station unknowns may be generated by rover 100 locally by a between-base station processor 140, which receives the positions of the base stations and their satellite navigation data from base station information to modulator 130. Processor 140 may implement the same methods described in greater detail in the below section entitled Between Base Station Processing, Part II. In addition, processor 140 may comprise its own instruction and data memory, or may be implemented as part of main processor 110, such as by being implemented as a sub-process executed by main processor 110.

[0074] Main processor 110 may be configured to implement any and above described embodiments by the instructions stored in instruction memory 112. We describe implementation of these embodiments with respect to FIG. 6, where certain of the steps may be omitted when not needed by a particular embodiment. In step 202, the locations X₁, X₂, X₃ of the base stations B1, B2, B3 are received by base-station information modulator 130 and conveyed to main processor 110. These locations, and the location of the rover station, are measured at the phase centers of the GPS antennas. Thus, RF antenna 102 and demodulator 130 provides means for receiving the locations of the first base station and the second base station. Also in step 202, main processor 110 generates an initial estimated location for rover 100, which is relatively course. This may be the center of the triangle formed by the base stations, or may be derived from a conventional single point GPS measurements (as opposed to a differential GPS measurement), or maybe generated by other means. The means for performing this step is provided by main processor 110 under the direction of an instruction set stored in memory 112.

[0075] In step 204, one of the base stations is selected as a primary base station (B1) to form a primary baseline with the Rover station. The selection may be arbitrary, or may be based upon which base station is the closest to the initial estimated location of the Rover. The other base stations are secondary base stations and form secondary baselines with the rover. The means for performing this step may be provided by the human user, as prompted by main processor 100 through keypad/display 115, or may be provided directly by main processor 110 under the direction of an instruction set stored in memory 112.

[0076] In step 206, main processor 110 is provided with the measured satellite-navigation data (e.g.,





and

) as received by the rover (r=0), the primary base station(r=1), and the secondary base station(s) (r=2,3) at one or more time moments k (epochs). The data is provided by the modulators 120 (for the Rover data) and 130 (for the base station data). Although these sets of data for each epoch k may be received at slightly different times (because the base stations are at different distances from the Rover), the data sets are time-stamped with the epoch identifier (which is conventional practice), and can be stored in a synchronized queue until all the data sets for the epoch are received. Also during this step, main processor 110 determines the positions of the satellites for these time moments from orbital predictions, and generate the computed ranges of the satellites to the rover and base stations based on the positions of the satellites and the stations. The means for performing this step is provided by main processor 110 under the direction of an instruction set stored in memory 112, with the computed information being stored in data memory 114.

[0077] In step 208, for each secondary base station, Rover 100 obtains a time offset representative of the time difference between the clocks of the primary and secondary base station (e.g., Δ_2,1τ_k, Δ_3,1τ_k) at the time moments k. Rover 100 may obtain this information by directly receiving it from the primary base station B1 by way of demodulator 130, or may obtain at this information by using between-base station processor 140 to generate it, as indicated above. Either of these approaches provides the means for obtaining these time differences. As used herein, the term "obtain" encompasses both the receiving of the information from an outside source (e.g., the primary base station) and the generating of the information locally by processor 140.

[0078] The next step 210 is optional, depending upon the embodiment being implemented. In this step, rover 100 obtains, for each secondary base station, a set of satellite-phase cycle ambiguities related to the baseline between the secondary and primary base stations for one or more of the frequency bands (e.g., L1 and L2) at the time moments k. These ambiguities may be in floating form (e.g, Δ_2,1N^L1,s, NΔ_2,1N^L2,s, Δ_3,1N^L1,s, Δ_3,1N^L2,s), fixed-integer form (e.g, Δ_2,1N̂^L1,s, Δ_2,1N̂^L2,s, Δ_3,1N̂L^1,s, Δ_3,1N̂^L2,s) or integer plus fractional phase form (e.g., Δ_2,1N^L1,s, Δ_2,1Ψ^L1; Δ_2,1N^L2,s, Δ_2,1ψ^L2; Δ_3,1N^L1,s, Δ_3,1ψ^L1; Δ_3,1N^L2,s, Δ_3,1ψ^L2). Rover 100 may obtain this information by directly receiving it from the primary base station B1 by way of demodulator 130, or may obtain at this information by using between-base station processor 140 to generate it, as indicated above. Either of these approaches provides the means for obtaining this information. As used herein, the term "obtain" encompasses both the receiving of the information from an outside source (e.g., the primary base station) and the generating the information locally with processor 140.

[0079] In step 212, which is optional depending upon the embodiment, main processor 110 generates tropospheric difference terms

at the time moments k, which are to be used in the residuals. In the step, main processor 110 also generates the observation matrices for each time moment k. The means for performing this step is provided by main processor 110 under the direction of an instruction set stored in memory 112, with the difference terms being stored in data memory 114.

[0080] In step 214, main processor 110 generates the sets of residuals of the single-difference navigation equations (e.g.,





and

) associated with the primary baseline (R-B1) at the time moments k, and generates the sets of residuals of the single-difference navigation equations associated with the secondary baseline(s) (R-B2, R-B3) at the time moments k. The forms for generating these residuals were described above, and depend upon the embodiment being implemented. The means for generating the residuals is provided by main processor 110 under the direction of an instruction set stored in memory 112, with the residuals being stored in data memory 114.

[0081] As an optional step 216, main processor 110 generates ionosphere corrections and adds corrections to the residuals. The means for performing this step is provided by main processor 110 under the direction of an instruction set stored in memory 112, with the corrections being stored in data memory 114.

[0082] Finally, in step 218, main processor 110 estimates estimate the rover's location at the one or more time moments k from the sets of residuals, the time offset between the clocks of the base stations, the sets of satellite-phase cycle ambiguities related to the baseline between the primary base station and the secondary base stations (optional), and an observation matrix. The estimation may be done by the previously-described methods. The means for performing this estimation step is provided by main processor 110 under the direction of an instruction set stored in memory 112, with the computed information being stored in data memory 114.

[0083] Keypad/display 115 may be used to receive an instruction from the human user to commence an estimation of the position of the Rover, and to provide an indication of the estimated position of the Rover to the user. For some applications, it may be appreciated that human and interaction is not required and that the keyboard/display would be replaced by another interface component, as needed by the application.

Preferred Floating Ambiguity Resolution Process

[0084] We demonstrate the preferred floating ambiguity resolution process using forms [12'] -[17'] above. It may be appreciated that the other previously-described embodiments of the present invention may use also this floating ambiguity resolution process by simply omitting forms and/or terms of forms from the process. The general view of the preferred ambiguity resolution process is to reduce the value of the following form during a series of epochs:

In form F_Σ, Δ_1,0N_k represent the combined vector of current estimates of floating ambiguities: Δ_1,0N_k = [Δ_1,0N^L1, Δ_1,0N_k^L2], and the following are used for the cases of

and

We have also broken down the weighting matrices

etc., as follows:

etc. All of the other terms used above have been previously described with the exception of covariance matrix σ_1,0 and matrix D. The between station ionosphere delay, generally denoted here as

usually follows the Gauss-Markov time model:

where

τ_e is the time between successive epochs [sec], τ_I is the ionosphere model correlation time [sec], Δ_q,rε_k is white noise with the zero mean value and the variance of-

where

where, α ∈ [1,5] is a scaling parameter depending on the solar activity. Covariance matrix σ_1,0 is a diagonal matrix of all the individual values

and where the inverse square [σ_1,0]^-2 of the covariance matrix is a diagonal matrix of the inverse squares

of the individual values

Since this process is only accounting for the second order effects in the ionosphere delay differentials (rather than the full amount), the value of α is generally 2 to 3 times smaller than the value used in a single baseline ambiguity resolution process which accounts for the full amount.

[0085] In form [31], the term

is a cost function which effectively averages the floating ambiguities over several epochs by introducing a penalty if the set of estimated floating ambiguities Δ_1,0N̅_k at the k-th epoch is too far different from the previous estimated set. Δ_1,0N_k-1. With each successive epoch, the weighting matrix D_k-1 is generally made to be more convex. The second term of F_Σ generates the weighted sum of the squared residuals of forms [13A], [15A'], and [17A']. In a similar manner, the third term of F_Σ generates the weighted sum of the squared residuals of forms [13B'], [15B'], and [17B'], the fourth term generates the weighted sum of the squared residuals of forms [13C'], [15C'], and [17C'], and the fifth term generates the weighted sum of the squared residuals of forms [13D'], [15D'], and [17D']. The residual of each of the above forms of [13'], [15'], and [17'] is the difference between the right-hand side and left-hand side of the form. The weights are defined by the corresponding inverse covariance matrices.

[0086] An exemplary estimation process for the floating ambiguities according to the present invention employs form [31] in an iterative manner. We start at the initial epoch k=0 with the weighting matrix Do set to the zero matrix, and an initial guess of floating ambiguities Δ_1,0N₀ equal to zero. The first term of form [31] evaluates to zero for this initial epoch. We then generate a set of values for δX_k, Δ_1,0τ_k, δ_1,0I_k, Δ_1,0N_k at a first epoch k=1 which moves the value of F_Σ towards zero. This generates an initial estimate Δ_1,0N₁ for the floating ambiguities and the rover's position (by way of δX₁). A weighting matrix D₁ for the ambiguities is then generated, and a new set of values is generated for δX_k, Δ_1,0τ_k δ_1,0I_k, Δ_1,0N_k the next epoch k=2 which moves value of F_Σ (k=2) towards zero. As a result, subsequent estimates Δ_1,0N₂ and δX₂ are generated. This iteration process continues, with Δ_1,0N_k and δX_k generally improving in accuracy as the iterations progress.

[0087] Generating the values of δX_k, Δ_1,0τ_k, δ_1,0I_k, Δ_1,0N_k to minimize form [31] can be done in the following manner. Form [31] is constructed in a manner whereby each term is generally of the form: (M·Y -b)^T ·W· (M·Y-b), where Y is a vector of unknowns (e.g., some or all of δX_k, Δ_1,0τ_k, δ_1,0I_k, Δ_1,0N_k), M is a matrix of constants which multiply the unknowns (e.g., A_k, c), b is a vector of known values (e.g.,



), and W is a weighting matrix (e.g., D_k,

). The term (M·Y -b)^T ·W· (M·Y-b) can be reduced in value towards zero by generating a vector Y which satisfies the relationship (M^T·W·M)·Y = M^T·W·b, which we can simplify as H·Y = B. If H is not singular, we may apply an LU-decomposition method on H to find Y. The contributions of the six terms of form [31] may be synthesized according to the following form:

where H₀₀ is a 3-by-3 matrix with the following form:

where H₁₀ is a 1-by-3 row vector with the following form:

where H₂₀ is an N-by-3 matrix with the following form:

where H₃₀ is a 2N-by-3 matrix with the following form:

where h₁₁ is a 1-by-1 matrix with the following form:

where h₂₁ is an N-by-3 matrix with the following form:

where h₃₁ is a 2N-by-1 column vector with the following form:

where H₂₂ is an N-by-N matrix with the following form:

where H₃₂ is a 2N-by-N matrix with the following form:

where H₃₃ is a 2N-by-2N matrix with the following form:

where B_0,k is a 3-by-1 column vector with the forms:

where B_1,k is a single value with the forms:

where B_2,k is an N-by-1 column vector with the forms:

and where B_3,k is a 2N-by-1 column vector with the form:

The matrix H_k of form [32] is symmetric, and can be decomposed by a Cholesky factorization process into the form:

Then, the unknown vector

can be generated by a conventional forward and backward substitution processes by generating an intermediate matrix Ỹ from the form L_k Ỹ = B_k, and then generating matrix Y_k from L_k^T Y_k = Ỹ, where

This generates an updated set of floating ambiguities and updated rover position. Next, matrix D_k for the next iteration is generated as follows: D_k = L₃₃,_k L₃₃^T_k. The next iteration is then started by generating a new matrix H based on another epoch of data, and thereafter reiterating the above steps. While the epochs of data are generally processed in sequential time order, that is not a requirement of the present invention. In a post-processing situation, the epochs may be processed in any order. It can be shown that the matrix D_k = L_33,k L₃₃^T_k is mathematically equivalent to the following form:

Matrix D_k is the matrix of the second partial derivatives of the cost function F_Σ (δX_k, Δ_1,0τ_k, δ_1,0I_k, Δ_1,0N_k) partially minimized with respect to the variables δX_k, Δ_1,0τ_k, δ_1,0I_k :

[0088] The above process of generating the values of δX_k , Δ_1,0τ_k δ_1,0I_k, and Δ_1,0N_k which minimizes the cost function F_Σ (δX_k, Δ_1,0τ_k, δ_1,0I_k, Δ_1,0N_k) generates an estimate for the position of Rover as X₀ = (X₀ + δX_k), which has an accuracy which is acceptable for many applications. Higher accuracy generally results if we generate a set of fixed-integer ambiguities Δ_1,0N̂_k from the floating ambiguities Δ_1,0N_k, and generate an estimate of the rover position from the fixed-integer ambiguities. Examples of this are described in the next section.

[0089] The means for performing then above steps in rover 100 are provided by main processor 110 under the direction of instruction sets stored in memory 112, with the various computed data being stored in data memory 114.

Fixed-Integer Ambiguity Resolution

[0090] Having at hand the estimation of the floating ambiguities Δ_1,0N_k, we describe an inventive method of generating the fixed-integer ambiguities

which may be used alone or in combination with the processes described above. The components of the vector Δ_1,0N̂_L1,k have the same fractional part Δψ^L1, and the components of vector Δ_1,0N̂_L2,k have the same fractional part Δψ^L2. Having at hand the matrix D_k and the vector Δ_1,0N_k, the embodiment forms the following cost function form:

The embodiment generates the values of Δ_1,0N̂_k which minimize the value of F(Δ_1,0N̂_k) subject to the conditions:

and

where Z^nk denotes the domain of integer valued vectors (vectors having only integer components). To generate the values of Δ_1,0N̂_k, two reference satellites ŝ^L1 and ŝ^L2 are selected for the first and the second frequency bands. A between-satellite double difference matrix Σ is then generated, and will be applied to matrix Δ_1,0N_k. Matrix E comprises a 2N-by-2N identity matrix, but with the columns associated with satellites ŝ^L1 and ŝ^L2 being modified, as shown below:

The columns are modified by substituting a value of -1 for each column element that would normally be zero in the identity matrix. The positions of columns of matrix E which are associated with satellites ŝ¹ and ŝ² correspond to the row positions of these satellites in the vector Δ_1,0N_k. When matrix Σ is multiplied onto vector Δ_1,0N_k, the floating ambiguities corresponding to satellites ŝ^L1 and ŝ^L2 remain unchanged, but the floating ambiguity associated with ŝ^L1 is subtracted from the other floating ambiguities in the L1-band, and the floating ambiguity associated with ŝ^L2 is subtracted from the other floating ambiguities in the L2-band. Next, a permutation matrix Π is generated, and is applied to matrix Σ to generated a matrix product Π·Σ. Permutation matrix is constructed to move the ŝ¹ and ŝ² columns of matrix E to the first and second column positions of the matrix product Π·Σ. The construction of permutation matrices is well known to the field of mathematics. A permutation matrix satisfies the following relationships: Π^T·Π = Π·Π^T = I. Next, a change of variables for the cost function F is undertaken as follows:

and the cost function can be formed as:

The first two components of M̂_k are real valued components (floating point numbers) and the remaining 2N-2 components are integers. Let us divide the matrix G_k into appropriate blocks in accordance with division of the vectors

and

where G_11,k is a 2-by-2 matrix, G_21,k is a 2-by-(2N-2) matrix, and where G_22,k is a (2N-2)-by-(2N-2) matrix. This partitioning enables us to use a two step process of minimizing

by first generating values of M̂_1,k that reduce the value of F(M̂_k), and thereafter generating values of M̂_2,k that further reduce the value of F(M̂_k). We notate this two step process as:

The first step (inner minimization) of generating M̂_1,k to reduce F(M̂_k) is performed in the space of floating point numbers (real valued space), and generates M̂_1,k in a form equivalent to:

the second step (outer minimization) of generating M̂_2,k is performed by substituting the form [41] of M̂_1,k into form [40] to generate the following modified version thereof:

Then, a search of an integer subspace for values of M̂_2,k is performed to find a set of integers which provides the smallest value of the modified form [42]. The integer subspace can be relatively small, and centered about the floating point values of M_2,k. After the integer search of form [42] is performed, the result M̂_2,k is substituted into form [41] to generate a revised vector M̂_1,k. Then, the change of variables operation (form [38]) is reversed as follows to generate the fixed-integer ambiguities Δ_1,0N̂_k as:

Δ_1,0N̂_k may then be separated into its components

and

[0091] As an option, an ambiguity resolution validation procedure may be performed to check for consistency in the ambiguity resolution. This procedure is conventional, and the reader is referred to prior art literature for a description thereof.

[0092] Having resolved the fixed-integer ambiguities, we can new generate a further refined estimate of the other solvable unknowns: δX_k, Δ_1,0τ_k, δ_1,0I_k. A third cost function is formed as follows:

where the five terms of the form are the same as the second through sixth terms of form [31], except that floating ambiguities have been replaced by the fixed-integer ambiguities. The same estimation procedures used on form [31] may be applied above to form [44], except that only one iteration is needed, and matrix D is not generated.

[0093] The means for performing then above steps in rover 110 are provided by main processor 110 under the direction of instruction sets stored in memory 112, with the various computed data being stored in data memory 114.

[0094] If lower accuracy can be tolerated, we may apply the process on form [44] using the floating point ambiguities rather than the fixed-integer ambiguities. In this case, the above fixed-integer ambiguity resolution process may be omitted.

Between Base Station Processing, Part II

[0095] In the above embodiments, the data of forms [6] and/or [7] were provided to the rover station. However, because several of the rover-to-base station processes described above are more efficient than those in the prior art, it is possible for the rover itself to undertake the task of generating some or all of forms [6] and [7] at the rover location, in real-time, from phase and pseudo-range measurements conveyed from the base stations to the rover. This information may be conveyed by radio-signals from the base stations to the rover, as described above. One may also implement a system whereby the base stations convey their information to a relay station by cable (such as the internet), with the relay station positioned within a few kilometers of the rover station. The relay station then relays the base station data to the rover by radio-signals.

[0096] In these embodiments, the rover receives the following data from each base station "r" (r = 1, 2, 3) for several epochs

and

The locations of the base stations are also obtained: X₁, X₂, and X₃. As indicated previously, the locations of the satellites are highly predictable and can readily be determined by the rover with its clock and correction data from the almanac data transmitted by the satellites. From this, the rover generates the computed ranges

from each rover "r" to each satellite "s" of a group of satellites being tracked. As before, the troposphere delay terms are estimated from the Goad-Goodman model.

[0097] With this information, the residuals (difference quantities)



and

of forms [4A-4D] are generated for each baseline (q, r), where (q, r) has the following pairings (B2, B1), (B3, B1), and (B2, B3). For each baseline, the solvable unknowns in forms [5A-5D] are Δ_q,rτ_k, Δ_q,rI_k, and Δ_q,rN_k, Values are estimated from the residuals in a manner similar to that described about for the primary baseline between the Rover and first base station. As an example, a cost function F(*) may be formed as follows:

wherein the covariance matrices

σ_q,r are generated in a similar manner as the covariance matrices for the primary baseline.

[0098] The floating ambiguities may be estimated in an iterative manner as described above. We start at the initial epoch k=0 with the weighting matrix Do set to the zero matrix, and an initial guess of floating ambiguities Δ_q,rN₀ equal to zero. The first term of form [31] evaluates to zero for this initial epoch. We then generate a set of values for Δ_q,rτ_k, Δ_q,rI_k, Δ_q,rN_k, at a first epoch k=1 which moves the value of F towards zero. This generates an initial estimate Δ_q,rN₁ for the floating ambiguities. A weighting matrix D₁ for the ambiguities is then generated, and a new set of values is generated for Δ_q,rτ_k, Δ_q,rI_k, Δ_q,rN_k at the next epoch k=2 which moves value of F (k=2) towards zero. As a result, subsequent estimates Δ_q,rN₂, is generated. This iteration process continues, with Δ_q,rN_k generally improving in accuracy as the iterations progress. The corresponding H·Y = B form for this process (similar to form [32]) is as follows:

where h₁₁ is a 1-by-1 matrix with the following form:

where h₂₁ is an N-by-3 matrix with the following form:

where h₃₁ is a 2N-by-1 column vector with the following form:

where H₂₂ is an N-by-N matrix with the following form:

where H₃₂ is a 2N-by-N matrix with the following form:

where H₃₃ is a 2N-by-2N matrix with the following form:

where B_1,k is a single value with the forms:

where B_2,k is an N-by-1 column vector with the forms:

and where B_3,k is a 2N-by-1 column vector with the form:

The matrix H_k of form [46] is symmetric, and can be decomposed by a Cholesky factorization process into the form:

Then, the unknown vector

can be generated by a conventional forward and backward substitution processes by generating an intermediate matrix Ỹ from the form L_k Ỹ = B_k, and then generating matrix Y_k from L_k^TY_k = Ỹ, where

This generates an updated set of floating ambiguities and updated rover position. Next, matrix D_k for the next iteration is generated as follows: D_k = L_33,k L₃₃^T_k. The next iteration is then started by generating a new matrix H based on another epoch of data, and thereafter reiterating the above steps. While the epochs of data are generally processed in sequential time order, that is not a requirement of the present invention. In a post-processing situation, the epochs may be processed in any order. It can be shown that the matrix D_k = L_33,k L₃₃^T_k is mathematically equivalent to the following form:

Matrix D_k is the matrix of the second partial derivatives of the cost function F(Δ_q,rτ_k, Δ_q,rI_k, Δ_q,rN_k,) partially minimized with respect to the variables Δ_q,rτ_k, Δ_q,rI_k:

where

The corresponding fixed-integer ambiguities Δ_q,rN̂_k, may be generated from the floating ambiguities Δ_q,rN_k, by the same process described above with reference to forms [37] - [43] that is used to generate the fixed-integer ambiguities associated with the primary base line between the rover (R) and first base station (B1).

[0099] Having resolved the fixed-integer ambiguities, we can new generate a further refined estimate of the other solvable unknowns: Δ_q,rτ_k, and Δ_q,rI_k. A third cost function is formed as follows:

where the five terms of the form are the same as the second through sixth terms of form [45], except that floating ambiguities have been replaced by the fixed-integer ambiguities. The same estimation procedures used on form [45] may be applied above to form [51], except that only one iteration is needed, and matrix D is not generated or used. As a result, estimates for and Δ_q,rI_k are generated. However, we prefer to perform some consistency checks on these estimates before providing to the process that operates on the primary baseline between the rover and the first base station. Thus, we will denote these estimates with hat symbols as follows: Δ_q,rτ̂_k, and Δ_q,rÎ_k, After the estimates associated with the three base line (q,r) = (B2, B1), (B3, B1), (B3, B1) have been generated for the k-th epoch, we have the following data:

Δ_2,1τ̂_k, Δ_2,1Î_k, Δ_2,1N̂_k,

Δ_3,1τ̂_k, Δ_3,1Î_k, Δ_3,1N̂_k, and

Δ_3,2τ̂_k, Δ_3,2Î_k, Δ_3,2N̂_k.

We first perform an ambiguity resolution closure check. In this check, the following relationships should hold:

which is equivalent to:

If the above relationships are not satisfied, the ambiguities have been resolved incorrectly for at least one base line, and the estimations of fixed ambiguity should be neglected. To address an incorrect resolution, new data may be taken, various subsets of data may be processes to generate sets of ambiguities which satisfy the above relationships. After all three between base receivers ambiguity have been resolved and the above relationships are satisfied, the ambiguity vectors Δ_2,1N̂_k, Δ_3,1N̂_k, and Δ_3,2N̂_k, are considered to be correctly fixed.

[0100] The time delays are similarly checked and corrected by taking new data or searching existing data sets. In this check, the following relationships should hold:

which is equivalent to: Δ_2,1τ̂_k + Δ_3,2τ̂_k- Δ_3,1τ̂_k = 0, to within a tolerance value of ±∈₁, [53B]
where ∈₁ is a tolerance level which is close to zero. In general, ∈₁ depends upon the distances between baselines and the desired degree of accuracy for the system. If the above relationships hold, then we validate these delays (i.e., Δ_2,1τ_k = Δ_2,1τ̂_k, Δ_3,1τ_k = Δ_3,1τ̂_k, and Δ_3,2τ_k = Δ_3,2τ̂_k).

[0101] Next, we perform a consistency check on the ionosphere delays. In the following discussion, we the subscripts on the ionosphere delay differentials have sometimes been exchanged, but this is of no substantive consequence since Δ_1,2Î_k = Δ_2,1Î_k, Δ_2,3Î_k = -Δ_3,2Î_k and Δ_1,3Î_k = -Δ_3,1Î_k. The between base receivers ionosphere estimations should satisfy the relationship

However, measurements noise typically prevents these relationships from being satisfied to an acceptable tolerance level ±∈₂. To better satisfy [54], the following quadratic function is minimized to obtain new estimations Δ_1,2Ĩ_k, Δ_2,3Ĩ_k Δ_3,1Ĩ_k:

provided the condition of:

is satisfied. The ionosphere estimations covariance matrices C_1,2,C_2,3,C_3,1 are estimated in the previous process by conventional methods. The inventors have found that the following form minimizes form [55] subject to condition [56]:

Before applying form [57], the vectors Δ_1,2Î_k, Δ_2,3Î_k, Δ_3,1Î_k are preferably smoothed using Kalman filtering scheme with a dynamic model based the above described the Gauss-Markov time model (forms [GM1] and [GM2] above).

[0102] The results of these process may be provided to the process which generates the ionosphere delay differentials for the baselines associated with the rover stations, specifically the differentials generated according to forms [26], [29], and [30]. For form [26], which generates Δ_1,0Ĩ_k, the results are provided as follows: Δ_1,2I_k = Δ_1,2Ĩ_k and Δ_1,3Î_k = Δ_1,3Ĩ_k For generating the ionosphere delay differentials according to form [29] we set Δ_2,1I_k = -Δ_1,2Ĩ_k. For generating the ionosphere delay differentials according to form [30] we set Δ_3,1I_k = Δ_3,1Ĩ_k.

[0103] Thus, to summarize a preferred embodiment of the present invention, at each epoch "k" the following occurs for the three baselines between the base stations:

• Update of the floating ambiguity estimates by way of forms [45]-[50],
• Generate fixed-integer ambiguities (with a process similar to that illustrated by forms [37] - [43]);
• Generate estimates of Δ_q,rτ_k and Δ_q,rI_k by way of form [51] with a process similar to that illustrated by forms [45]-[50]
• Check consistency of the ambiguities (Δ_2,1 N̂_k + Δ_3,2N̂_k + Δ_1,2N̂_k = 0) and time offsets Δ_2,1τ̂_k Δ_3,2τ̂_k Δ_1,3τ̂_k = 0);
• Generate adjusted estimates Δ_1,2Ĩ_k,Δ_2,3Ĩ_k,Δ_3,1Ĩ_k of the ionosphere delay differentials;
• Provide these results to the process of estimating the rover's position using the primary and secondary baselines.

[0104] The above base-station to base-station data can be generated by the rover, or by an external source, such as relay station. In the case of rover 100, the means for performing all of the above steps are provided by Between-Base Station processor 140 under the direction of instruction sets stored in an instruction memory, with the various computed data being stored in a data memory. Moreover, while higher accuracy is obtained by generating the fixed-integer ambiguities, lower accuracy embodiments may just generate the floating ambiguities.

[0105] While it is preferable to interpolate the ionosphere delays using two baselines between three base stations, it may be appreciated that some application may achieve acceptable accuracy by only interpolating the ionosphere delays using one baseline between two base stations. Such an example may be a road project where the road is relatively straight, as shown in FIG. 4.

[0106] Each of the above methods of generating the base station data and estimating the coordinates of the rover is preferably implemented by a data processing system, such as a microcomputer, operating under the direction of a set of instructions stored in computer-readable medium, such as ROM, RAM, magnetic tape, magnetic disk, etc. All the methods may be implements on one data processor, or they may be divided among two or data processors.

Computer Program Products

[0107] It may be appreciated that each of the above methods may comprise the form of a computer program to be installed in a computer for controlling the computer to perform the process for estimating the location of a rover station (R) with the use of at least a first base station (B1) and a second base station (B2), with the process comprising the various steps of the method.

[0108] In addition, each of the above methods of generating the base station data and estimating the coordinates of the rover may be implemented by a respective computer program product which directs a data processing system, such as a microcomputer, to perform the steps of the methods. Each computer program product comprises a computer-readable memory, such for example as ROM, RAM, magnetic tape, magnetic disk, etc., and a plurality of sets of instructions embodied on the computer-readable medium, each set directing the data processing system to execute a respective step of the method being implemented. FIG. 7 shows an exemplary comprehensive listing of instructions sets for implementing the above method. Each of the above methods is achieved by selecting the corresponding groups of instruction sets (as apparent from the above discussions). Instruction set #18 is common to all of the methods, and is modified to omit the data which is not used by the particular method.

[0109] While the present invention has been particularly described with respect to the illustrated embodiments, it will be appreciated that various alterations, modifications and adaptations may be made based on the present disclosure, and are intended to be within the scope of the present invention. While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiments, it is to be understood that the present invention is not limited to the disclosed embodiments but, on the contrary, is intended to be limited only by the scope of the appended claims.

Claims

1. A method of estimating the location of a rover station (R) with the use of a first base station (B1) and a second base station (B2), the method comprising:

(a) (202) receiving known locations of the first base station and the second base station;

(b) (206) receiving measured satellite navigation data as received by the rover station, the first base station, and the second base station;

(c) (208) obtaining a first time offset representative of a difference between a first offset from true GPS time of the clock of the first base station and a second offset from true GPS time of the clock of the second base station;

(d) (214) generating a first set of residuals of differential navigation equations associated with a first baseline (R-B1) between the rover station and the first base station, the residuals being related to the measured satellite navigation data received by the rover station and the first base station, the locations of the satellites, and the locations of the rover station and the first base station;

(e) (214) generating a second set of residuals of differential navigation equations associated with a second baseline (R-B2) between the rover station and the second base station, the residuals being related to the measured satellite navigation data received by the rover station and the second base station, the locations of the satellites, and the locations of the rover station and the second base station;

(f) substituting, within the second set of residuals, an unknown time offset associated with the second baseline (R-B2) with a value composed of a sum of the first time offset and a time offset associated with the first baseline (R-B1); and

(g) (218) generating, subsequent to the substitution step of (f), an estimate of the rover station's location from the first set of residuals, the second set of residuals and the first time offset.

2. The method of Claim 1 further comprising the steps of:

(h) (202) receiving the location of a third base station (B3);

(i) (206) receiving measured satellite navigation data as received by the third base station; and

(j) (208) obtaining a second time offset representative of the difference between the first offset from true GPS time of the clock of the first base station and a third offset from true GPS time of the clock of the third base station;

(k) (214) generating a third set of residuals of differential navigation equations associated with a third baseline (R-B3) between the rover station and the third base station, the residuals being related to the satellite navigation data received by the rover station and the third base station, the locations of the satellites, and the locations of the rover station and the third base station;

(1) substituting, within the third set of residuals, an unknown time offset associated with the third baseline (R-B3) with a value composed of a sum of the second time offset and a time offset associated with the first baseline (R-B1); and

wherein step (g) generates, subsequent to the substitution step of (1), the estimate of the rover station's location further from the third set of residuals and the second time offset.

3. The method of Claim 1 wherein step (c) comprises the step of generating the first time offset.

4. The method of Claim 2 wherein step (c) comprises the step of generating the first time offset and wherein step (j) comprises the step of generating the second time offset.

5. The method of Claim 4 further comprising the steps of generating a third time offset representative of a difference between the second offset from true GPS time of the clock of the second station and the third offset from true GPS time of the clock of the third base station, and comparing the sum of the first time offset, the second time offset and the third time offset around a loop of the base stations to the value of zero.

6. The method of Claim 1 or claim 2 wherein the first and second sets of residuals are based on pseudo-range data, and wherein said method further comprises the step of generating a first set of carrier-phase-based residuals of differential navigation equations for the first baseline (R-B1) between the rover station and the first base station, the first set of carrier-phase-based residuals being related to at least the measured satellite carrier-phase data received by the rover station and the first base station, the locations of the satellites, and the locations of the rover station and the first base station; and
wherein step (g) generates the estimate of the rover station's location further from the first set of carrier-phase-based residuals.

7. The method of Claim 6 further comprising the steps of:

obtaining a first set of satellite carrier-phase cycle ambiguities associated with the baseline between the first and second base stations;

generating a second set of carrier-phase-based residuals of differential navigation equations associated with the second baseline (R-B2) between the rover station and the second base station, the second set of carrier-phase-based residuals being related to at least the measured satellite carrier-phase data received by the rover station and the second base station, the locations of the satellites, and the locations of the rover station and the second base station; and

wherein step (g) generates the estimate of the rover station's location further from the second set of carrier-phase-based residuals and the first set of satellite-phase cycle ambiguities.

8. The method of Claim 7 wherein claim 6 is dependent on claim 2, further comprising the steps of:

obtaining a second set of satellite carrier-phase cycle ambiguities associated with the baseline between the first and third base stations;

generating a third set of carrier-phase-based residuals of differential navigation equations associated with the third baseline (R-B3) between the rover station and the third base station, the third set of carrier-phase-based residuals being related to at least the measured satellite carrier-phase data received by the rover station and the third base station, the locations of the satellites, and the locations of the rover station and the third base station; and

wherein step (g) generates the estimate of the rover station's location further from the third set of carrier-phase-based residuals and the second set of satellite-phase cycle ambiguities.

9. The method of Claim 6 further comprising the step of generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals and at least one of the sets of residuals based on pseudo-range data; and
wherein step (g) generates the estimate of the rover station's location further from the first set of floating ambiguities.

10. The method of Claim 6 further comprising the steps of:

generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals and at least one of the sets of residuals based on pseudo-range data; and

generating a first set of fixed-integer floating ambiguities for the baseline between the rover station and first base station from the first set of floating ambiguities;

wherein step (g) generates the estimate of the rover station's location further from the first set of fixed-integer floating ambiguities.

11. The method of Claim 7 further comprising the step of:

generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals, the second set of carrier-phase-based residuals, the first set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, and at least one of the sets of residuals based on pseudo-range data;

wherein step (g) generates the estimate of the rover station's location further from the first set of floating ambiguities.

12. The method of Claim 6 further comprising the steps of:

generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals, the second set of carrier-phase-based residuals, the first set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, and at least one of the sets of residuals based on pseudo-range data;

generating a first set of fixed-integer floating ambiguities for the baseline between the rover station and first base station from the first set of floating ambiguities;

wherein step (g) generates the estimate of the rover station's location further from the first set of fixed-integer floating ambiguities.

13. The method of Claim 8 further comprising the step of:

generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals, the second set of carrier-phase-based residuals, the first set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, the third set of carrier-phase-based residuals, the second set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, and at least one of the sets of residuals based on pseudo-range data;

wherein step (g) generates the estimate of the rover station's location further from the first set of floating ambiguities.

14. The method of Claim 8 further comprising the steps of:

generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals, the second set of carrier-phase-based residuals, the first set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, the third set of carrier-phase-based residuals, the second set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, and at least one of the sets of residuals based on pseudo-range data;

generating a first set of fixed-integer floating ambiguities for the baseline between the rover station and first base station from the first set of floating ambiguities;

wherein step (g) generates the estimate of the rover station's location further from the first set of fixed-integer floating ambiguities.

15. The method according to any of the above claims further comprising the steps of:

obtaining a first set of first ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and second base stations, and

generating corrections to one or more of the residuals, the corrections being related to the first set of first ionosphere delay differentials, the locations of the first and second base stations, and an estimated location of the rover station; and

modifying said one or more of the residuals with said corrections.

16. The method according to claim 8 further comprising the steps of:

obtaining a first set of first ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and second base stations,

obtaining a second set of second ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and third base stations, and

generating corrections to one or more of the residuals, the corrections being related to the first set of first ionosphere delay differentials, the second set of second ionosphere delay differentials, the locations of the base stations, and an estimated location of the rover station; and

modifying said one or more of the residuals with said corrections.

17. The method of Claim 16 wherein the correction to the residuals associated with satellite "s" in one or both of the second set of residuals and the second set of carrier-phase-based residuals is related to the quantity

where

is the first ionosphere delay differential associated with satellite "s", and

is an estimated ionosphere delay differential associated with satellite "s" along the baseline between the rover station and first base station.

18. The method of Claim 16 wherein the correction to the residuals associated with satellite "s" in one or both of the third set of residuals and the third set of carrier-phase-based residuals is related to the quantity

where

is the second ionosphere delay differential associated with satellite "s", and

is an estimated ionosphere delay differential associated with satellite "s" along the baseline between the rover station and first base station.

19. The method of Claim 16 wherein the ionosphere delay differential from the first set and associated with satellite "s" may be denoted as

wherein the ionosphere delay differential from the second set and associated with satellite "s" may be denoted as

wherein the locations of the first, second, and third base stations may be represented by the vectors X₁, X₂, and X₃ , and wherein the estimated location of the rover station may be represented as X_0,k,
wherein the corrections to one or more of the residuals associated with satellite "s" are related to a quantity

where

wherein α and β are constants that satisfy the relationships:



where notation { * }_n denotes the component of the bracketed quantity along the north direction, where notation { * }_e denotes the component of the bracketed quantity along the east direction.

20. The method of Claim 19 wherein the correction to the residuals associated with satellite "s" in one or both of the second set of residuals and the second set of carrier-phase-based residuals is related to the quantity

where

is the first ionosphere delay differential associated with satellite "s".

21. The method of Claim 19 wherein the correction to the residual associated with satellite "s" in one or both of the third set of residuals and the third set of carrier-phase-based residuals is related to the quantity

where

is the second ionosphere delay differential associated with satellite "s".

22. The method according to Claim 16 further comprising the steps of:

modifying one or more of the above residuals to be dependent upon second order effects in the ionosphere delay corrections applied to the baselines associated with the rover station, and

generating an estimate of the second order effects, and

wherein step (g) generates the estimate of the rover station's location further from the estimated second order effects.

23. The method according to Claim 16 wherein the method generates the first set of first ionosphere delay differentials and the second set of second ionosphere delay differentials from at least the navigation data that it receives from the base stations.

24. The method according to Claim 16 further comprising the steps of:

generating an initial estimate of the first set of first ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and second base stations;

generating an initial estimate of second set of second ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and third base stations;

generating an initial estimate of a third set of third ionosphere delay differentials associated with the satellite signals received along the baseline formed by the second and third base stations; and

generating final estimates of the ionosphere delay differentials such that the sum of the final estimates of the first, second, and third ionosphere delay differentials for at least one satellite "s" around a loop of the base stations is substantially zero.

25. The method of Claim 7 wherein the step of obtaining the first set of satellite carrier-phase cycle ambiguities comprises the step of generating the first set of satellite carrier-phase cycle ambiguities from at least the locations of the base stations, and measured satellite navigation data as received by the base stations.

26. The method of Claim 8 wherein the steps of obtaining the first and second sets of satellite carrier-phase cycle ambiguities comprises the step of generating the first set of satellite carrier-phase cycle ambiguities from at least the locations of the first and second base stations and measured satellite navigation data as received by the first and second base stations, and the step of generating the second set of satellite carrier-phase cycle ambiguities from at least the locations of the first and third base stations and measured satellite navigation data as received by the first and third base stations.

27. The method of Claim 26 further comprising the steps of generating a third set of satellite carrier-phase cycle ambiguities associated with the baseline between the second and third base stations, and comparing the sum of the three sets of satellite carrier-phase ambiguities around a loop of the base stations to the value of zero.

28. A computer program which, when run on a computer processor, causes the computer processor to carry out the method of any preceding claim.

29. An apparatus for estimating the location of a rover station (R) with the use of a first base station (B1) and a second base station (B2), the apparatus comprising:

(a) means for receiving the locations of the first base station and the second base station;

(b) means for receiving measured satellite navigation data as received by the rover station, the first base station, and the second base station;

(c) means for obtaining a first time offset representative of a difference between a first offset from true GPS time of the clock of the first base station and a second offset from true GPS time of the clock of the second base station;

(d) means for generating a first set of residuals of differential navigation equations associated with a first baseline (R-B1) between the rover station and the first base station, the residuals being related to the measured satellite navigation data received by the rover station and the first base station, the locations of the satellites, and the locations of the rover station and the first base station;

(e) means for generating a second set of residuals of differential navigation equations associated with a second baseline (R-B2) between the rover station and the second base station, the residuals being related to the measured satellite navigation data received by the rover station and the second base station, the locations of the satellites, and the locations of the rover station and the second base station; and

(f) means for substituting, within the second set of residuals, an unknown time offset associated with the second baseline (R-B2) with a value composed of a sum of the first time offset and a time offset associated with the first baseline (R-B1); and

(g) means for generating , subsequent to the substitution of step (f), an estimate of the rover station's location from the first set of residuals, the second set of residuals and the first time offset.

30. The apparatus of Claim 29 further comprising:

(h) means for receiving the location of a third base station;

(i) means for receiving measured satellite navigation data as received by the third base station;

(j) means for obtaining a second time offset representative of the difference between the first offset from true GPS time of the clock of the first base station and a third offset from true GPS time of the clock of the third base station;

(k) means for generating a third set of residuals of differential navigation equations associated with a third baseline (R-B3) between the rover station and the third base station, the residuals being related to the satellite navigation data received by the rover station and the third base station, the locations of the satellites, and the locations of the rover station and the third base station;

(1) means for substituting, within the third set of residuals, an unknown time offset associated with the third baseline (R-B3) with a value composed of a sum of the second time offset and a time associated with the first baseline (R-B1); and

wherein the means (g) for generating, subsequent to the substitution step of (1), the estimate of the rover station's location generates the estimate further from the third set of residuals and the second time offset.

31. The apparatus of Claim 29 wherein the means (c) for obtaining the first time offset comprises means for generating the first time offset.

32. The apparatus of Claim 30 wherein the means (c) for obtaining the first time offset comprises means for generating the first time offset and wherein the means (j) for obtaining the second time offset comprises means for generating the second time offset.

33. The apparatus of Claim 32 further comprising means for generating a third time offset representative of the time difference between the second offset from true GPS time of the clock of the second base station and the third offset from true GPS time of the clock of the third base station, and means for comparing the sum of the first time offset, the second time offset, and the third time offset around a loop of the base stations to the value of zero.

34. The apparatus of Claim 29 or claim 30 wherein the first and second sets of residuals are based on pseudo-range data, and wherein the apparatus further comprises means for generating a first set of carrier-phase-based residuals of differential navigation equations for the first baseline (R-B1) between the rover station and the first base station, the first set of carrier-phase-based residuals being related to at least the measured satellite carrier-phase data received by the rover station and the first base station, the locations of the satellites, and the locations of the rover station and the first base station; and
wherein the means (g) for generating the estimate of the rover station's location generates the estimate further from the first set of carrier-phase-based residuals.

35. The apparatus of Claim 34 further comprising:

means for obtaining a first set of satellite carrier-phase cycle ambiguities associated with the baseline between the first and second base stations;

means for generating a second set of carrier-phase-based residuals of differential navigation equations associated with the second baseline (R-B2) between the rover station and the second base station, the second set of carrier-phase-based residuals being related to at least the measured satellite carrier-phase data received by the rover station and the second base station, the locations of the satellites, and the locations of the rover station and the second base station; and

wherein the means (g) for generating the estimate of the rover station's location generates the estimate further from the second set of carrier-phase-based residuals and the first set of satellite-phase cycle ambiguities.

36. The apparatus of Claim 35 wherein claim 34 is dependent on claim 30 further comprising:

means for obtaining a second set of satellite carrier-phase cycle ambiguities associated with the baseline between the first and third base stations;

means for generating a third set of carrier-phase-based residuals of differential navigation equations associated with the third baseline (R-B3) between the rover station and the third base station, the third set of carrier-phase-based residuals being related to at least the measured satellite carrier-phase data received by the rover station and the third base station, the locations of the satellites, and the locations of the rover station and the third base station; and

wherein the means (g) for generating the estimate of the rover station's location generates the estimate further from the third set of carrier-phase-based residuals and the second set of satellite-phase cycle ambiguities.

37. The apparatus of Claim 32 further comprising means for generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals and at least one of the sets of residuals based on pseudo-range data; and
wherein the means (g) for generating the estimate of the rover station's location generates the estimate further from the first set of floating ambiguities.

38. The apparatus of Claim 34 further comprising:

means for generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals and at least one of the sets of residuals based on pseudo-range data; and

means for generating a first set of fixed-integer floating ambiguities for the baseline between the rover station and first base station from the first set of floating ambiguities;

wherein the means (g) for generating the estimate of the rover station's location generates the estimate further from the first set of fixed-integer floating ambiguities.

39. The apparatus of Claim 35 further comprising:

means for generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals, the second set of carrier-phase-based residuals, the first set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, and at least one of the sets of residuals based on pseudo-range data;

wherein the means (g) for generating the estimate of the rover station's location generates the estimate further from the first set of floating ambiguities.

40. The apparatus of Claim 35 further comprising:

means for generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals, the second set of carrier-phase-based residuals, the first set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, and at least one of the sets of residuals based on pseudo-range data; and

means for generating a first set of fixed-integer floating ambiguities for the baseline between the rover station and first base station from the first set of floating ambiguities;

wherein the means (g) for generating the estimate of the rover station's location generates the estimate further from the first set of fixed-integer floating ambiguities.

41. The apparatus of Claim 36 further comprising:

means for generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals, the second set of carrier-phase-based residuals, the first set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, the third set of carrier-phase-based residuals, the second set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, and at least one of the sets of residuals based on pseudo-range data;

wherein the means (g) for generating the estimate of the rover station's location generates the estimate further from the first set of floating ambiguities.

42. The apparatus of Claim 36 further comprising:

means for generating a first set of floating ambiguities for the baseline between the rover station and first base station from the first set of carrier-phase-based residuals, the second set of carrier-phase-based residuals, the first set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, the third set of carrier-phase-based residuals, the second set of satellite carrier-phase cycle ambiguities related to the baseline between the first and second base stations, and at least one of the sets of residuals based on pseudo-range data; and

means for generating a first set of fixed-integer floating ambiguities for the baseline between the rover station and first base station from the first set of floating ambiguities;

wherein the means (g) for generating the estimate of the rover station's location generates the estimate further from the first set of fixed-integer floating ambiguities.

43. The apparatus according to any of the above claims 29 - 42 further comprising:

means for obtaining a first set of first ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and second base stations, and

means for generating corrections to one or more of the residuals, the corrections being related to the first set of first ionosphere delay differentials, the locations of the first and second base stations, and an estimated location of the rover station; and

means for modifying said one or more of the residuals with said corrections.

44. The apparatus according to claim 36 further comprising:

means for obtaining a first set of first ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and second base stations,

means for obtaining a second set of second ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and third base stations, and

means for generating corrections to one or more of the residuals, the corrections being related to the first set of first ionosphere delay differentials, the second set of second ionosphere delay differentials, the locations of the base stations, and an estimated location of the rover station; and

means for modifying said one or more of the residuals with said corrections.

45. The apparatus of Claim 44 wherein the correction to the residuals associated with satellite "s" in one or both of the second set of residuals and the second set of carrier-phase-based residuals is related to the quantity

where

is the first ionosphere delay differential associated with satellite "s", and

is an estimated ionosphere delay differential associated with satellite "s" along the baseline between the rover station and first base station.

46. The apparatus of Claim 44 wherein the correction to the residuals associated with satellite "s" in one or both of the third set of residuals and the third set of carrier-phase-based residuals is related to the quantity

where

is the second ionosphere delay differential associated with satellite "s", and

is an estimated ionosphere delay differential associated with satellite "s" along the baseline between the rover station and first base station.

47. The apparatus of Claim 44 wherein the ionosphere delay differential from the first set and associated with satellite "s" may be denoted as

wherein the ionosphere delay differential from the second set and associated with satellite "s" may be denoted as

wherein the locations of the first, second, and third base stations may be represented by the vectors X₁, X₂, and X₃, and wherein the estimated location of the rover station may be represented as X_0,k,
wherein the corrections to one or more of the residuals associated with satellite "s" are related to a quantity

where

wherein α and β are constants that satisfy the relationships:



where notation { * }_n denotes the component of the bracketed quantity along the north direction, where notation {* }_e denotes the component of the bracketed quantity along the east direction.

48. The apparatus of Claim 44 wherein the correction to the residuals associated with satellite "s" in one or both of the second set of residuals and the second set of carrier-phase-based residuals is related to the quantity

where

is the first ionosphere delay differential associated with satellite "s".

49. The apparatus of Claim 44 wherein the correction to the residual associated with satellite "s" in one or both of the third set of residuals and the third set of carrier-phase-based residuals is related to the quantity

where

is the second ionosphere delay differential associated with satellite "s".

50. The apparatus according to Claim 43 further comprising:

means for modifying one or more of the above residuals to be dependent upon second order effects in the ionosphere delay corrections applied to the baselines associated with the rover station, and

means for generating an estimate of the second order effects, and

wherein the means (i) for generating the estimate of the rover station's location generates the estimate further from the estimated second order effects.

51. The apparatus according to Claim 43 wherein the apparatus generates the first set of first ionosphere delay differentials and the second set of second ionosphere delay differentials from at least the navigation data that it receives from the base stations.

52. The apparatus according to Claim 43 further comprising:

means for generating an initial estimate of the first set of first ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and second base stations;

means for generating an initial estimate of second set of second ionosphere delay differentials associated with the satellite signals received along the baseline formed by the first and third base stations;

means for generating an initial estimate of a third set of third ionosphere delay differentials associated with the satellite signals received along the baseline formed by the second and third base stations; and

means for generating final estimates of the ionosphere delay differentials such that the sum of the final estimates of the first, second, and third ionosphere delay differentials for at least one satellite "s" around a loop of the base stations is substantially zero.

53. The apparatus of Claim 35 wherein the means for obtaining the first set of satellite carrier-phase cycle ambiguities comprises means for generating the first set of satellite carrier-phase cycle ambiguities from at least the locations of the base stations, and measured satellite navigation data as received by the base stations.

54. The apparatus of Claim 36 wherein the means for obtaining the first and second sets of satellite carrier-phase cycle ambiguities comprises means for generating the first set of satellite carrier-phase cycle ambiguities from at least the locations of the first and second base stations and measured satellite navigation data as received by the first and second base stations, and means for generating the second set of satellite carrier-phase cycle ambiguities from at least the locations of the first and third base stations and measured satellite navigation data as received by the first and third base stations.

Ansprüche

1. Verfahren zum Abschätzen des Standortes einer Erkundungsstation (R) unter Verwendung einer ersten Basisstation (B1) und einer zweiten Basisstation (B2), wobei das Verfahren umfasst:

(a) (202) Empfangen bekannter Standorte der ersten Basisstation und der zweiten Basisstation;

(b) (206) Empfangen gemessener Satellitennavigationsdaten, wie durch die Erkundungsstation, die erste Basisstation und die zweite Basisstation empfangen;

(c) (208) Erhalten eines ersten Zeitabstands, repräsentativ für einen Unterschied zwischen einem ersten Abstand von einer wahren GPS-Zeit der Uhr der ersten Basisstation und einem zweiten Abstand von einer wahren GPS-Zeit von der Uhr der zweiten Basisstation;

(d) (214) Erzeugen eines ersten Satzes von Residuen von Differenzialnavigationsgleichungen, welche einer ersten Basislinie (R-B1) zwischen der Erkundungsstation und der ersten Basisstation zugeordnet sind, wobei die Residuen in Beziehung stehen mit den von der Erkundungsstation und der ersten Basisstation empfangenen gemessenen Satellitennavigationsdaten, den Standorten der Satelliten und den Standorten der Erkundungsstation und der ersten Basisstation;

(e) (214) Erzeugen eines zweiten Satzes von Residuen von Differenzialnavigationsgleichungen, welche einer zweiten Basislinie (R-B2) zwischen der Erkundungsstation und der zweiten Basisstation zugeordnet sind, wobei die Residuen in Beziehung stehen mit den von der Erkundungsstation und der zweiten Basisstation empfangenen gemessenen Satellitennavigationsdaten, den Standorten der Satelliten und den Standorten der Erkundungsstation und der zweiten Basisstation;

(f) Substituieren, innerhalb des zweiten Satzes von Residuen, eines unbekannten Zeitabstands, welcher der zweiten Basislinie (R-B2) zugeordnet ist, mit einem Wert, welcher aus einer Summe des ersten Zeitabstands und eines Zeitabstands, welcher der ersten Basislinie (R-B1) zugeordnet ist, zusammengesetzt ist; und

(g) (218) Erzeugen, dem Substitutionsschritt von (f) nachfolgend, eine Abschätzung des Standortes der Erkundungsstation aus dem ersten Satz von Residuen, dem zweiten Satz von Residuen und dem ersten Zeitabstand.

2. Verfahren nach Anspruch 1 ferner umfassend die Schritte:

(h) (202) Empfangen des Standortes einer dritten Basisstation (B3);

(i) (206) Empfangen gemessener Satellitennavigationsdaten, wie durch die dritte Basisstation empfangen; und

(j) (208) Erhalten eines zweiten Zeitabstands, repräsentativ für den Unterschied zwischen dem ersten Abstand von einer wahren GPS-Zeit von der Uhr der ersten Basisstation und einem dritten Abstand von einer wahren GPS-Zeit von der Uhr der dritten Basisstation;

(k) (214) Erzeugen eines dritten Satzes von Residuen von Differenzialnavigationsgleichungen, welche einer dritten Basislinie (R-B3) zwischen der Erkundungsstation und der dritten Basisstation zugeordnet sind, wobei die Residuen in Beziehung stehen mit den von der Erkundungsstation und der dritten Basisstation empfangenen Satellitennavigationsdaten, den Standorten der Satelliten und den Standorten der Erkundungsstation und der dritten Basisstation;

(I) Substituieren, innerhalb des dritten Satzes von Residuen, eines unbekannten Zeitabstands, welcher der dritten Basislinie (R-B3) zugeordnet ist, mit einem Wert, welcher aus einer Summe des zweiten Zeitabstands und eines Zeitabstands, welcher der ersten Basislinie (R-B1) zugeordnet ist, zusammengesetzt ist; und

wobei Schritt (g), dem Substitutionsschritt (I) nachfolgend, die Abschätzung des Standortes der Erkundungsstation ferner aus dem dritten Satz von Residuen und dem zweiten Zeitabstand erzeugt.

3. Verfahren nach Anspruch 1, wobei Schritt (c) den Schritt eines Erzeugens des ersten Zeitabstands umfasst.

4. Verfahren nach Anspruch 2, wobei Schritt (c) den Schritt eines Erzeugens des ersten Zeitabstands umfasst und wobei Schritt (j) den Schritt eines Erzeugens des zweiten Zeitabstands umfasst.

5. Verfahren nach Anspruch 4, ferner umfassend die Schritte eines Erzeugens eines dritten Zeitabstands, repräsentativ für einen Unterschied zwischen dem zweiten Abstand von einer wahren GPS-Zeit von der Uhr der zweiten Station und des dritten Abstands von einer wahren GPS-Zeit von der Uhr der dritten Basisstation und Vergleichen der Summe des ersten Zeitabstands, des zweiten Zeitabstands und des dritten Zeitabstands ringsum einer Schlaufe von den Basisstationen mit dem Wert von null.

6. Verfahren nach Anspruch 1 oder Anspruch 2, wobei der erste und zweite Satz von Residuen auf Pseudoabstandsdaten basieren und wobei das Verfahren ferner den Schritt eines Erzeugens eines ersten Satzes von trägerphasenbasierten Residuen von Differenzialnavigationsgleichungen für die erste Basislinie (R-B1) zwischen der Erkundungsstation und der ersten Basisstation umfasst, wobei der erste Satz von trägerphasenbasierten Residuen in Bezug steht zu mindestens den gemessenen Satellitenträgerphasendaten, welche durch die Erkundungsstation und die erste Basisstation empfangen werden, den Standorten der Satelliten, und den Standorten der Erkundungsstation und der ersten Basisstation; und
wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus dem ersten Satz von trägerphasenbasierten Residuen erzeugt.

7. Verfahren nach Anspruch 6, ferner umfassend die Schritte:

Erhalten eines ersten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche der Basislinie zwischen der ersten und zweiten Basisstation zugeordnet sind;

Erzeugen eines zweiten Satzes von trägerphasenbasierten Residuen von Differenzialnavigationsgleichungen, welche der zweiten Basislinie (R-B2) zwischen der Erkundungsstation und der zweiten Basisstation zugeordnet sind, wobei der zweite Satz von trägerphasenbasierten Residuen in Bezug steht mit mindestens den gemessenen Satellitenträgerphasendaten, welche durch die Erkundungsstation und die zweite Basisstation empfangen werden, den Standorten der Satelliten, und den Standorten der Erkundungsstation und der zweiten Basisstation; und

wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus dem zweiten Satz von trägerphasenbasierten Residuen und dem ersten Satz von Satellitenphasenzyklusmehrdeutigkeiten erzeugt.

8. Verfahren nach Anspruch 7, wobei Anspruch 6 von Anspruch 2 abhängig ist, ferner umfassend die Schritte:

Erhalten eines zweiten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten, welcher der Basislinie zwischen der ersten und dritten Basisstation zugeordnet sind;

Erzeugen eines dritten Satzes von trägerphasenbasierten Residuen von Differenzialnavigationsgleichungen, welche der dritten Basislinie (R-B3) zwischen der Erkundungsstation und der dritten Basisstation zugeordnet sind, wobei der dritte Satz von trägerphasenbasierten Residuen in Beziehung steht mindestens mit den gemessenen Satellitenträgerphasendaten, welche durch die Erkundungsstation und die dritte Basisstation empfangen werden, den Standorten der Satelliten, und den Standorten der Erkundungsstation und der dritten Basisstation; und

wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus dem dritten Satz von trägerphasenbasierten Residuen und dem zweiten Satz von Satellitphasenzyklusmehrdeutigkeiten erzeugt.

9. Verfahren nach Anspruch 6, ferner umfassend den Schritt eines Erzeugens eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren; und
wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus dem ersten Satz von Fließkommamehrdeutigkeiten erzeugt.

10. Verfahren nach Anspruch 6, ferner umfassend die Schritte:

Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren; und

Erzeugen eines ersten Satzes von Fest-Integer-Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von Fließkommamehrdeutigkeiten;

wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus dem ersten Satz von Fest-Integer-Fließkommamehrdeutigkeiten erzeugt.

11. Verfahren nach Anspruch 7, ferner umfassend den Schritt:

Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von trägerphasenbasierten Residuen, dem ersten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche in Beziehung stehen zu der Basislinie zwischen der ersten und zweiten Basisstation, und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren;

wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus dem ersten Satz von Fließkommamehrdeutigkeiten erzeugt.

12. Verfahren nach Anspruch 6, ferner umfassend die Schritte:

Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von trägerphasenbasierten Residuen, dem ersten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche in Beziehung stehen zu der Basislinie zwischen der ersten und zweiten Basisstation, und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren;

Erzeugen eines ersten Satzes von Fest-Integer-Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von Fließkommamehrdeutigkeiten;

wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus dem ersten Satz von Fest-Integer-Fließkommamehrdeutigkeiten erzeugt.

13. Verfahren nach Anspruch 8, ferner umfassend den Schritt:

Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von trägerphasenbasierten Residuen, dem ersten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche in Beziehung stehen zu der Basislinie zwischen der ersten und zweiten Basisstation, dem dritten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche mit der Basislinie zwischen der ersten und zweiten Basisstation in Beziehung stehen, und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren;

wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus dem ersten Satz von Fließkommamehrdeutigkeiten erzeugt.

14. Verfahren nach Anspruch 8, ferner umfassend die Schritte:

Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von trägerphasenbasierten Residuen, dem ersten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche mit der Basislinie zwischen der ersten und zweiten Basisstation in Beziehung stehen, dem dritten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche mit der Basislinie zwischen der ersten und zweiten Basisstation in Beziehung stehen, und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren;

Erzeugen eines ersten Satzes von Fest-Integer-Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von Fließkommamehrdeutigkeiten;

wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus dem ersten Satz von Fest-Integer-Fließkommamehrdeutigkeiten erzeugt.

15. Verfahren nach einem der vorhergehenden Ansprüche, ferner umfassend die Schritte:

Erhalten eines ersten Satzes von ersten lonosphärenverzögerungsdifferentialen, welche den entlang einer zwischen der ersten und zweiten Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind, und

Erzeugen von Korrekturen für ein oder mehrere aus den Residuen, wobei die Korrekturen in Beziehung stehen mit dem ersten Satz von ersten lonosphärenverzögerungsdifferentialen, den Standorten der ersten und zweiten Basisstation und einem abgeschätzten Standort der Erkundungsstation; und

Modifizieren des einen oder der mehreren aus den Residuen mit den Korrekturen.

16. Verfahren nach Anspruch 8, ferner umfassend die Schritte:

Erhalten eines ersten Satzes von ersten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die erste und zweite Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind,

Erhalten eines zweiten Satzes von zweiten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die erste und dritte Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind, und

Erzeugen von Korrekturen für ein oder mehrere aus den Residuen, wobei die Korrekturen in Beziehung stehen mit dem ersten Satz von ersten lonosphärenverzögerungsdifferentialen, dem zweiten Satz von zweiten Ionosphärenverzögerungsdifferentialen, den Standorten der Basisstationen und einem abgeschätzten Standort der Erkundungsstation; und

Modifizieren des einen oder der mehreren aus den Residuen mit den Korrekturen.

17. Verfahren nach Anspruch 16, wobei die Korrektur für die Residuen, welche einem Satelliten "s" in einem oder beiden von dem zweiten Satz von Residuen und dem zweiten Satz von trägerphasenbasierten Residuen zugeordnet sind, in Beziehung steht zu der Größe

wobei

das einem Satelliten "s" zugeordnete erste lonosphärenverzögerungsdifferential ist, und

ein abgeschätztes lonosphärenverzögerungsdifferential ist, welches einem Satelliten "s" zugeordnet ist, entlang der Basislinie zwischen der Erkundungsstation und ersten Basisstation.

18. Verfahren nach Anspruch 16, wobei die Korrektur für die Residuen, welche einem Satelliten "s" in einem oder beiden von dem dritten Satz von Residuen und dem dritten Satz von trägerphasenbasierten Residuen zugeordnet sind, in Beziehung steht zu der Größe

wobei

das einem Satelliten "s" zugeordnete zweite Ionosphärenverzögerungsdifferential ist, und

ein abgeschätztes lonosphärenverzögerungsdifferential ist, welches einem Satelliten "s" zugeordnet ist, entlang der Basislinie zwischen der Erkundungsstation und ersten Basisstation.

19. Verfahren nach Anspruch 16, wobei das lonosphärenverzögerungsdifferential aus dem ersten Satz und zugeordnet Satellit "s" bezeichnet werden kann als

wobei das lonosphärenverzögerungsdifferential aus dem zweiten Satz und zugeordnet Satellit "s" bezeichnet werden kann als

wobei die Standorte der ersten, zweiten und dritten Basisstationen durch Vektoren X₁, X₂ und X₃ repräsentiert werden können, und wobei der abgeschätzte Standort der Erkundungsstation durch X_0,k repräsentiert werden kann,

wobei die Korrekturen für ein oder mehrere aus den Residuen, welche einem Satelliten "s" zugeordnet sind, in Beziehung stehen zu einer Größe

wobei

wobei α und β Konstanten sind, welche die Beziehungen erfüllen:

wobei eine Schreibweise {_*}_n die Komponente der in Klammern gesetzten Größe entlang der Nordrichtung bezeichnet, wobei eine Schreibweise {*}_e die Komponente der in Klammern gesetzten Größe entlang der Ostrichtung bezeichnet.

20. Verfahren nach Anspruch 19, wobei die Korrektur der einem Satelliten "s" zugeordneten Residuen, in einem oder beiden aus dem zweiten Satz von Residuen und dem zweiten Satz von trägerphasenbasierten Residuen, in Beziehung steht mit der Größe

wobei

das erste einem Satelliten "s" zugeordnete lonosphärenverzögerungsdifferential ist.

21. Verfahren nach Anspruch 19, wobei die Korrektur des einem Satelliten "s" zugeordneten Residuums, in einem oder beiden aus den dritten Satz von Residuen und dem dritten Satz von trägerphasenbasierten Residuen, in Beziehung steht mit der Größe

wobei

das zweite einem Satelliten "s" zugeordnete lonosphärenverzögerungsdifferential ist.

22. Verfahren nach Anspruch 16, ferner umfassend die Schritte:

Modifizieren eines oder mehrerer der obigen Residuen, um abhängig von Effekten zweiter Ordnung in den lonosphärenverzögerungskorrekturen zu sein, welche an den Basislinien appliziert werden, welche der Erkundungsstation zugeordnet sind, und

Erzeugen einer Abschätzung der Effekte zweiter Ordnung, und

wobei Schritt (g) die Abschätzung des Standortes der Erkundungsstation ferner aus den abgeschätzten Effekten zweiter Ordnung erzeugt.

23. Verfahren nach Anspruch 16, wobei das Verfahren den ersten Satz von ersten lonosphärenverzögerungsdifferentialen und den zweiten Satz von zweiten lonosphärenverzögerungsdifferentialen aus mindestens den Navigationsdaten erzeugt, welches es von den Basisstationen empfängt.

24. Verfahren nach Anspruch 16, ferner umfassend die Schritte:

Erzeugen einer Initialabschätzung des ersten Satzes von ersten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die erste und zweite Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind;

Erzeugen einer Initialabschätzung eines zweiten Satzes von zweiten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die erste und dritte Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind;

Erzeugen einer Initialabschätzung eines dritten Satzes von dritten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die zweite und dritte Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind; und

Erzeugen finaler Abschätzungen der lonosphärenverzögerungsdifferentiale, sodass die Summe der finalen Abschätzung der ersten, zweiten und dritten lonosphärenverzögerungsdifferentiale für mindestens einen Satelliten "s", ringsum einer Schlaufe der Basisstationen, im Wesentlichen null ist.

25. Verfahren nach Anspruch 7, wobei der Schritt eines Erhaltens des ersten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten den Schritt eines Erzeugens des ersten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten aus mindestens den Standorten der Basisstationen und gemessener Satellitennavigationsdaten, wie durch die Basisstationen empfangen, umfasst.

26. Verfahren nach Anspruch 8, wobei die Schritte eines Erhaltens der ersten und zweiten Sätze von Satellitenträgerphasenzyklusmehrdeutigkeiten den Schritt eines Erzeugens des ersten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten aus mindestens den Standorten der ersten und zweiten Basisstation und gemessenen Satellitennavigationsdaten, wie durch die erste und zweite Basisstation empfangen, und den Schritt eines Erzeugens des zweiten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten aus mindestens den Standorten der ersten und dritten Basisstation und gemessener Satellitennavigationsdaten, wie durch die erste und dritte Basisstation empfangen, umfasst.

27. Verfahren nach Anspruch 26, ferner umfassend die Schritte eines Erzeugens eines dritten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche der Basislinie zwischen der zweiten und dritten Basisstation zugeordnet sind und Vergleichen der Summe von den drei Sätzen von Satellitenträgerphasenmehrdeutigkeiten mit einem Wert von null, ringsum einer Schlaufe der Basisstationen.

28. Computerprogramm, welches, wenn es auf einem Computerprozessor läuft, den Computerprozessor dazu veranlasst, das Verfahren nach einem der vorhergehenden Ansprüche auszuführen.

29. Vorrichtung zum Abschätzen des Standortes einer Erkundungsstation (R) unter Verwendung einer ersten Basisstation (B1) und einer zweiten Basisstation (B2), wobei die Vorrichtung umfasst:

(a) Mittel zum Empfangen der Standorte der ersten Basisstation und der zweiten Basisstation;

(b) Mittel zum Empfangen gemessener Satellitennavigationsdaten, wie durch die Erkundungsstation, die erste Basisstation und die zweite Basisstation empfangen;

(c) Mittel zum Erhalten eines ersten Zeitabstands, repräsentativ für einen Unterschied zwischen einem ersten Abstand von einer wahren GPS-Zeit der Uhr der ersten Basisstation und einem zweiten Abstand von einer wahren GPS-Zeit von der Uhr der zweiten Basisstation;

(d) Mittel zum Erzeugen eines ersten Satzes von Residuen von Differenzialnavigationsgleichungen, welche einer ersten Basislinie (R-B1) zwischen der Erkundungsstation und der ersten Basisstation zugeordnet sind, wobei die Residuen in Beziehung stehen mit den von der Erkundungsstation und der ersten Basisstation empfangenen gemessenen Satellitennavigationsdaten, den Standorten der Satelliten und den Standorten der Erkundungsstation und der ersten Basisstation;

(e) Mittel zum Erzeugen eines zweiten Satzes von Residuen von Differenzialnavigationsgleichungen, welche einer zweiten Basislinie (R-B2) zwischen der Erkundungsstation und der zweiten Basisstation zugeordnet sind, wobei die Residuen in Beziehung stehen mit den von der Erkundungsstation und der zweiten Basisstation empfangenen gemessenen Satellitennavigationsdaten, den Standorten der Satelliten und den Standorten der Erkundungsstation und der zweiten Basisstation; und

(f) Mittel zum Substituieren, innerhalb des zweiten Satzes von Residuen, eines unbekannten Zeitabstands, welcher der zweiten Basislinie (R-B2) zugeordnet ist, mit einem Wert, welcher aus einer Summe des ersten Zeitabstands und eines Zeitabstands, welcher der ersten Basislinie (R-B1) zugeordnet ist, zusammengesetzt ist; und

(g) Mittel zum Erzeugen, dem Substitutionsschritt von (f) nachfolgend, eine Abschätzung des Standortes der Erkundungsstation aus dem ersten Satz von Residuen, dem zweiten Satz von Residuen und dem ersten Zeitabstand.

30. Vorrichtung nach Anspruch 29 ferner umfassend:

(h) Mittel zum Empfangen des Standortes einer dritten Basisstation;

(i) Mittel zum Empfangen gemessener Satellitennavigationsdaten, wie durch die dritte Basisstation empfangen;

(j) Mittel zum Erhalten eines zweiten Zeitabstands, repräsentativ für den Unterschied zwischen dem ersten Abstand von einer wahren GPS-Zeit von der Uhr der ersten Basisstation und einem dritten Abstand von einer wahren GPS-Zeit von der Uhr der dritten Basisstation;

(k) Mittel zum Erzeugen eines dritten Satzes von Residuen von Differenzialnavigationsgleichungen, welche einer dritten Basislinie (R-B3) zwischen der Erkundungsstation und der dritten Basisstation zugeordnet sind, wobei die Residuen in Beziehung stehen mit den von der Erkundungsstation und der dritten Basisstation empfangenen Satellitennavigationsdaten, den Standorten der Satelliten und den Standorten der Erkundungsstation und der dritten Basisstation;

(I) Mittel zum Substituieren, innerhalb des dritten Satzes von Residuen, eines unbekannten Zeitabstands, welcher der dritten Basislinie (R-B3) zugeordnet ist, mit einem Wert, welcher aus einer Summe des zweiten Zeitabstands und einer Zeit, welche der ersten Basislinie (R-B1) zugeordnet ist, zusammengesetzt ist; und

wobei das Mittel (g) zum Erzeugen, dem Substitutionsschritt (I) nachfolgend, der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem dritten Satz von Residuen und dem zweiten Zeitabstand erzeugt.

31. Vorrichtung nach Anspruch 29, wobei das Mittel (c) zum Erhalten des ersten Zeitabstands ein Mittel für ein Erzeugen des ersten Zeitabstands umfasst.

32. Vorrichtung nach Anspruch 30, wobei das Mittel (c) zum Erhalten des ersten Zeitabstands ein Mittel für ein Erzeugen des ersten Zeitabstands umfasst und wobei das Mittel (j) zum Erhalten des zweiten Zeitabstands ein Mittel für ein Erzeugen des zweiten Zeitabstands umfasst.

33. Vorrichtung nach Anspruch 32, ferner umfassend ein Mittel für ein Erzeugen eines dritten Zeitabstands, repräsentativ für einen Zeitunterschied zwischen dem zweiten Abstand von einer wahren GPS-Zeit von der Uhr der zweiten Basisstation und des dritten Abstands von einer wahren GPS-Zeit von der Uhr der dritten Basisstation und ein Mittel zum Vergleichen der Summe des ersten Zeitabstands, des zweiten Zeitabstands und des dritten Zeitabstands, ringsum einer Schlaufe von den Basisstationen, mit dem Wert von null.

34. Vorrichtung nach Anspruch 29 oder Anspruch 30, wobei der erste und zweite Satz von Residuen auf Pseudoabstandsdaten basieren und wobei die Vorrichtung ferner ein Mittel für ein Erzeugen eines ersten Satzes von trägerphasenbasierten Residuen von Differenzialnavigationsgleichungen für die erste Basislinie (R-B1) zwischen der Erkundungsstation und der ersten Basisstation umfasst, wobei der erste Satz von trägerphasenbasierten Residuen in Bezug steht zu mindestens den gemessenen Satellitenträgerphasendaten, welche durch die Erkundungsstation und die erste Basisstation empfangen werden, den Standorten der Satelliten, und den Standorten der Erkundungsstation und der ersten Basisstation; und
wobei das Mittel (g) zum Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem ersten Satz von trägerphasenbasierten Residuen erzeugt.

35. Vorrichtung nach Anspruch 34, ferner umfassend:

Mittel zum Erhalten eines ersten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche der Basislinie zwischen der ersten und zweiten Basisstation zugeordnet sind;

Mittel zum Erzeugen eines zweiten Satzes von trägerphasenbasierten Residuen von Differenzialnavigationsgleichungen, welche der zweiten Basislinie (R-B2) zwischen der Erkundungsstation und der zweiten Basisstation zugeordnet sind, wobei der zweite Satz von trägerphasenbasierten Residuen in Bezug steht mit mindestens den gemessenen Satellitenträgerphasendaten, welche durch die Erkundungsstation und die zweite Basisstation empfangen werden, den Standorten der Satelliten, und den Standorten der Erkundungsstation und der zweiten Basisstation; und

wobei das Mittel (g) zum Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem zweiten Satz von trägerphasenbasierten Residuen und dem ersten Satz von Satellitenphasenzyklusmehrdeutigkeiten erzeugt.

36. Vorrichtung nach Anspruch 35, wobei Anspruch 34 von Anspruch 30 abhängig ist, ferner umfassend:

Mittel zum Erhalten eines zweiten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten, welcher der Basislinie zwischen der ersten und dritten Basisstation zugeordnet sind;

Mittel zum Erzeugen eines dritten Satzes von trägerphasenbasierten Residuen von Differenzialnavigationsgleichungen, welche der dritten Basislinie (R-B3) zwischen der Erkundungsstation und der dritten Basisstation zugeordnet sind, wobei der dritte Satz von trägerphasenbasierten Residuen in Beziehung steht mindestens mit den gemessenen Satellitenträgerphasendaten, welche durch die Erkundungsstation und die dritte Basisstation empfangen werden, den Standorten der Satelliten, und den Standorten der Erkundungsstation und der dritten Basisstation; und

wobei das Mittel (g) zum Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem dritten Satz von trägerphasenbasierten Residuen und dem zweiten Satz von Satellitphasenzyklusmehrdeutigkeiten erzeugt.

37. Vorrichtung nach Anspruch 32, ferner umfassend ein Mittel für ein Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren; und
wobei das Mittel (g) für ein Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem ersten Satz von Fließkommamehrdeutigkeiten erzeugt.

38. Vorrichtung nach Anspruch 34, ferner umfassend:

Mittel zum Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren; und

Mittel zum Erzeugen eines ersten Satzes von Fest-Integer-Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von Fließkommamehrdeutigkeiten;

wobei das Mittel (g) für ein Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem ersten Satz von Fest-Integer-Fließkommamehrdeutigkeiten erzeugt.

39. Vorrichtung nach Anspruch 35, ferner umfassend:

Mittel zum Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von trägerphasenbasierten Residuen, dem ersten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche in Beziehung stehen zu der Basislinie zwischen der ersten und zweiten Basisstation, und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren;

wobei das Mittel (g) für ein Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem ersten Satz von Fließkommamehrdeutigkeiten erzeugt.

40. Vorrichtung nach Anspruch 35, ferner umfassend:

Mittel zum Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von trägerphasenbasierten Residuen, dem ersten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche in Beziehung stehen zu der Basislinie zwischen der ersten und zweiten Basisstation, und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren; und

Mittel zum Erzeugen eines ersten Satzes von Fest-Integer-Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von Fließkommamehrdeutigkeiten;

wobei das Mittel (g) für ein Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem ersten Satz von Fest-Integer-Fließkommamehrdeutigkeiten erzeugt.

41. Vorrichtung nach Anspruch 36, ferner umfassend:

Mittel zum Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von trägerphasenbasierten Residuen, dem ersten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche in Beziehung stehen zu der Basislinie zwischen der ersten und zweiten Basisstation, dem dritten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche mit der Basislinie zwischen der ersten und zweiten Basisstation in Beziehung stehen, und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren;

wobei das Mittel (g) für ein Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem ersten Satz von Fließkommamehrdeutigkeiten erzeugt.

42. Vorrichtung nach Anspruch 36, ferner umfassend:

Mittel zum Erzeugen eines ersten Satzes von Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von trägerphasenbasierten Residuen, dem ersten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche mit der Basislinie zwischen der ersten und zweiten Basisstation in Beziehung stehen, dem dritten Satz von trägerphasenbasierten Residuen, dem zweiten Satz von Satellitenträgerphasenzyklusmehrdeutigkeiten, welche mit der Basislinie zwischen der ersten und zweiten Basisstation in Beziehung stehen, und mindestens einem aus den Sätzen von Residuen, welche auf Pseudoabstandsdaten basieren; und

Mittel zum Erzeugen eines ersten Satzes von Fest-Integer-Fließkommamehrdeutigkeiten für die Basislinie zwischen der Erkundungsstation und ersten Basisstation aus dem ersten Satz von Fließkommamehrdeutigkeiten;

wobei das Mittel (g) für ein Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus dem ersten Satz von Fest-Integer-Fließkommamehrdeutigkeiten erzeugt.

43. Vorrichtung nach einem der vorhergehenden Ansprüche 29-42, ferner umfassend:

Mittel zum Erhalten eines ersten Satzes von ersten lonosphärenverzögerungsdifferentialen, welche den entlang einer zwischen der ersten und zweiten Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind, und

Mittel zum Erzeugen von Korrekturen für ein oder mehrere aus den Residuen, wobei die Korrekturen in Beziehung stehen mit dem ersten Satz von ersten lonosphärenverzögerungsdifferentialen, den Standorten der ersten und zweiten Basisstation und einem abgeschätzten Standort der Erkundungsstation; und

Mittel zum Modifizieren des einen oder der mehreren aus den Residuen mit den Korrekturen.

44. Vorrichtung nach Anspruch 36, ferner umfassend:

Mittel zum Erhalten eines ersten Satzes von ersten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die erste und zweite Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind,

Mittel zum Erhalten eines zweiten Satzes von zweiten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die erste und dritte Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind, und

Mittel zum Erzeugen von Korrekturen für ein oder mehrere aus den Residuen, wobei die Korrekturen in Beziehung stehen mit dem ersten Satz von ersten lonosphärenverzögerungsdifferentialen, dem zweiten Satz von zweiten lonosphärenverzögerungsdifferentialen, den Standorten der Basisstationen und einem abgeschätzten Standort der Erkundungsstation; und

Mittel zum Modifizieren des einen oder der mehreren aus den Residuen mit den Korrekturen.

45. Vorrichtung nach Anspruch 44, wobei die Korrektur für die Residuen, welche einem Satelliten "s" in einem oder beiden von dem zweiten Satz von Residuen und dem zweiten Satz von trägerphasenbasierten Residuen zugeordnet sind, in Beziehung steht zu der Größe

wobei

das einem Satelliten "s" zugeordnete erste lonosphärenverzögerungsdifferential ist, und

ein abgeschätztes lonosphärenverzögerungsdifferential ist, welches einem Satelliten "s" zugeordnet ist, entlang der Basislinie zwischen der Erkundungsstation und ersten Basisstation.

46. Vorrichtung nach Anspruch 44, wobei die Korrektur für die Residuen, welche einem Satelliten "s" in einem oder beiden von dem dritten Satz von Residuen und dem dritten Satz von trägerphasenbasierten Residuen zugeordnet sind, in Beziehung steht zu der Größe

wobei

das einem Satelliten "s" zugeordnete zweite lonosphärenverzögerungsdifferential ist, und

ein abgeschätztes lonosphärenverzögerungsdifferential ist, welches einem Satelliten "s" zugeordnet ist, entlang der Basislinie zwischen der Erkundungsstation und ersten Basisstation.

47. Vorrichtung nach Anspruch 44, wobei das lonosphärenverzögerungsdifferential aus dem ersten Satz und zugeordnet Satellit "s" bezeichnet werden kann als

wobei das lonosphärenverzögerungsdifferential aus dem zweiten Satz und zugeordnet Satellit "s" bezeichnet werden kann als

wobei die Standorte der ersten, zweiten und dritten Basisstationen durch Vektoren X₁, X₂ und X₃ repräsentiert werden können, und wobei der abgeschätzte Standort der Erkundungsstation durch X_0,k repräsentiert werden kann,

wobei die Korrekturen für ein oder mehrere aus den Residuen, welche einem Satelliten "s" zugeordnet sind, in Beziehung stehen zu einer Größe

wobei

wobei α und β Konstanten sind, welche die Beziehungen erfüllen:

wobei eine Schreibweise {*}_n die Komponente der in Klammern gesetzten Größe entlang der Nordrichtung bezeichnet, wobei eine Schreibweise {*}_e die Komponente der in Klammern gesetzten Größe entlang der Ostrichtung bezeichnet.

48. Vorrichtung nach Anspruch 44, wobei die Korrektur der einem Satellit "s" zugeordneten Residuen, in einem oder beiden aus dem zweiten Satz von Residuen und dem zweiten Satz von trägerphasenbasierten Residuen, in Beziehung steht mit der Größe

wobei

das erste einem Satelliten "s" zugeordnete lonosphärenverzögerungsdifferential ist.

49. Vorrichtung nach Anspruch 44, wobei die Korrektur des einem Satelliten "s" zugeordneten Residuums, in einem oder beiden aus dem dritten Satz von Residuen und dem dritten Satz von trägerphasenbasierten Residuen, in Beziehung steht mit der Größe

wobei

das zweite einem Satelliten "s" zugeordnete lonosphärenverzögerungsdifferential ist.

50. Vorrichtung nach Anspruch 43, ferner umfassend:

Mittel zum Modifizieren eines oder mehrerer der obigen Residuen, um abhängig von Effekten zweiter Ordnung in den lonosphärenverzögerungskorrekturen zu sein, welche an den Basislinien appliziert werden, welche der Erkundungsstation zugeordnet sind, und

Mittel zum Erzeugen einer Abschätzung der Effekte zweiter Ordnung, und

wobei das Mittel (i) für ein Erzeugen der Abschätzung des Standortes der Erkundungsstation die Abschätzung ferner aus den abgeschätzten Effekten zweiter Ordnung erzeugt.

51. Vorrichtung nach Anspruch 43, wobei die Vorrichtung den ersten Satz von ersten lonosphärenverzögerungsdifferentialen und den zweiten Satz von zweiten lonosphärenverzögerungsdifferentialen aus mindestens den Navigationsdaten erzeugt, welches sie von den Basisstationen empfängt.

52. Vorrichtung nach Anspruch 43, ferner umfassend:

Mittel zum Erzeugen einer Initialabschätzung des ersten Satzes von ersten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die erste und zweite Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind;

Mittel zum Erzeugen einer Initialabschätzung eines zweiten Satzes von zweiten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die erste und dritte Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind;

Mittel zum Erzeugen einer Initialabschätzung eines dritten Satzes von dritten lonosphärenverzögerungsdifferentialen, welche den entlang der durch die zweite und dritte Basisstation ausgebildeten Basislinie empfangenen Satellitensignalen zugeordnet sind; und

Mittel zum Erzeugen finaler Abschätzungen der lonosphärenverzögerungsdifferentiale, sodass die Summe der finalen Abschätzung der ersten, zweiten und dritten lonosphärenverzögerungsdifferentiale für mindestens einen Satelliten "s", ringsum einer Schlaufe der Basisstationen, im Wesentlichen null ist.

53. Vorrichtung nach Anspruch 35, wobei das Mittel für ein Erhalten des ersten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten ein Mittel für ein Erzeugen des ersten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten aus mindestens den Standorten der Basisstationen und gemessener Satellitennavigationsdaten, wie durch die Basisstationen empfangen, umfasst.

54. Vorrichtung nach Anspruch 36, wobei das Mittel für ein Erhalten der ersten und zweiten Sätze von Satellitenträgerphasenzyklusmehrdeutigkeiten ein Mittel für ein Erzeugen des ersten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten aus mindestens den Standorten der ersten und zweiten Basisstation und gemessenen Satellitennavigationsdaten, wie durch die erste und zweite Basisstation empfangen, und ein Mittel für ein Erzeugen des zweiten Satzes von Satellitenträgerphasenzyklusmehrdeutigkeiten aus mindestens den Standorten der ersten und dritten Basisstation und gemessener Satellitennavigationsdaten, wie durch die erste und dritte Basisstation empfangen, umfasst.

Revendications

1. Procédé d'estimation de l'emplacement d'une station itinérante (R) à l'aide d'une première station de base (B1) et d'une deuxième station de base (B2), le procédé comprenant le fait de :

(a) recevoir (202) des emplacements connus de la première station de base et de la deuxième station de base ;

(b) recevoir (206) des données de navigation par satellite mesurées telles que reçues par la station itinérante, la première station de base, et la deuxième station de base ;

(c) obtenir (208) un premier décalage temporel représentant une différence entre un premier décalage par rapport à un temps GPS réel de l'horloge de la première station de base et un deuxième décalage par rapport au temps GPS réel de l'horloge de la deuxième station de base ;

(d) de générer (214) un premier ensemble de résidus d'équations de navigation différentielles associé à une première ligne de base (R-B1) entre la station itinérante et la première station de base, les résidus étant liés aux données de navigation par satellite mesurées qui sont reçues par la station itinérante et la première station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la première station de base ;

(e) générer (214) un deuxième ensemble de résidus d'équations de navigation différentielles associé à une deuxième ligne de base (R-B2) entre la station itinérante et la deuxième station de base, les résidus étant liés aux données de navigation par satellite mesurées qui sont reçues par la station itinérante et la deuxième station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la deuxième station de base ;

(f) remplacer, dans le deuxième ensemble de résidus, un décalage temporel inconnu associé à la deuxième ligne de base (R-B2) par une valeur composée d'une somme du premier décalage temporel et d'un décalage temporel associé à la première ligne de base (R- B1) ; et

(g) générer (218), à la suite de l'étape de substitution (f), une estimation de l'emplacement de la station itinérante à partir du premier ensemble de résidus, du deuxième ensemble de résidus et du premier décalage temporel.

2. Procédé de la revendication 1, comprenant en outre les étapes consistant à :

(h) recevoir (202) l'emplacement d'une troisième station de base (B3) ;

(i) recevoir (206) des données de navigation par satellite mesurées telles que reçues par la troisième station de base ; et

(j) obtenir (208) un deuxième décalage temporel représentant la différence entre le premier décalage temporel par rapport au temps GPS réel de l'horloge de la première station de base et un troisième décalage par rapport au temps GPS réel de l'horloge de la troisième station de base ;

(k) générer (214) un troisième ensemble de résidus d'équations de navigation différentielles associé à une troisième ligne de base (R-B3) entre la station itinérante et la troisième station de base, les résidus étant liés aux données de navigation par satellite reçues par la station itinérante et la troisième station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la troisième station de base ;

(1) remplacer, dans le troisième ensemble de résidus, un décalage temporel inconnu associé à la troisième ligne de base (R-B3) par une valeur composée d'une somme du deuxième décalage temporel et un décalage temporel associé à la première ligne de base (R- B1) ; et

dans lequel l'étape (g) génère, à la suite de l'étape de substitution (1), l'estimation de l'emplacement de la station itinérante davantage à partir du troisième ensemble de résidus et du deuxième décalage temporel.

3. Procédé de la revendication 1, dans lequel l'étape (c) comprend l'étape de génération du premier décalage temporel.

4. Procédé de la revendication 2, dans lequel l'étape (c) comprend l'étape de génération du premier décalage temporel et dans lequel l'étape (j) comprend l'étape de génération du deuxième décalage temporel.

5. Procédé de la revendication 4, comprenant en outre les étapes consistant à générer un troisième décalage temporel représentant une différence entre le deuxième décalage par rapport au temps GPS réel de l'horloge de la deuxième station et le troisième décalage par rapport au temps GPS réel de l'horloge de la troisième station de base, et à comparer la somme du premier décalage temporel, du deuxième décalage temporel et du troisième décalage temporel autour d'une boucle des stations de base à la valeur zéro.

6. Procédé de la revendication 1 ou 2, dans lequel les premier et deuxième ensembles de résidus sont basés sur des données de pseudo-distance, et dans lequel ledit procédé comprend en outre l'étape consistant à générer un premier ensemble de résidus basés sur la phase de porteuse d'équations de navigation différentielles pour la première ligne de base (R-B1) entre la station itinérante et la première station de base, le premier ensemble de résidus basés sur la phase de porteuse étant lié à au moins les données de phase de porteuse de satellite mesurées qui sont reçues par la station itinérante et la première station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la première station de base ; et
dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir du premier ensemble de résidus basés sur la phase de porteuse.

7. Procédé de la revendication 6, comprenant en outre les étapes consistant à :

obtenir un premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite associé à la ligne de base entre les première et deuxième stations de base ;

générer un deuxième ensemble de résidus basés sur la phase de porteuse d'équations de navigation différentielles associé à la deuxième ligne de base (R-B2) entre la station itinérante et la deuxième station de base, le deuxième ensemble de résidus basés sur la phase de porteuse étant lié à au moins les données de phase de porteuse de satellite mesurées qui sont reçues par la station itinérante et la deuxième station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la deuxième station de base ; et

dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir du deuxième ensemble de résidus basés sur la phase de porteuse et du premier ensemble d'ambiguïtés de cycle de phase de satellite.

8. Procédé de la revendication 7, dans lequel revendication 6 est dépendante de la revendication 2, comprenant en outre les étapes consistant à :

obtenir un deuxième ensemble d' ambiguïtés de cycle de phase de porteuse de satellite associé à la ligne de base entre les première et troisième stations de base ;

générer un troisième ensemble de résidus basés sur la phase de porteuse d'équations de navigation différentielles associé à la troisième ligne de base (R-B3) entre la station itinérante et la troisième station de base, le troisième ensemble de résidus basés sur la phase de porteuse étant lié à au moins les données de phase de porteuse de satellite mesurées qui sont reçues par la station itinérante et la troisième station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la troisième station de base ; et

dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir du troisième ensemble de résidus basés sur la phase de porteuse et du deuxième ensemble d'ambiguïtés de cycle de phase de satellite.

9. Procédé de la revendication 6, comprenant en outre l'étape consistant à générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance ; et
dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir du premier ensemble d'ambiguïtés flottantes.

10. Procédé de la revendication 6, comprenant en outre les étapes consistant à :

générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance; et

générer un premier ensemble d'ambiguïtés flottantes d'entier fixe pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble d'ambiguïtés flottantes ;

dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir du premier ensemble d'ambiguïtés flottantes d'entier fixe.

11. Procédé de la revendication 7, comprenant en outre l'étape consistant à :

générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble de résidus basés sur la phase de porteuse, du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance ;

dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir du premier ensemble d'ambiguïtés flottantes.

12. Procédé de la revendication 6, comprenant en outre les étapes consistant à :

générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble de résidus basés sur la phase de porteuse, du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance ;

générer un premier ensemble d'ambiguïtés flottantes d'entier fixe pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble d'ambiguïtés flottantes ;

dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir du premier ensemble d'ambiguïtés flottantes d'entier fixe.

13. Procédé de la revendication 8, comprenant en outre l'étape consistant à :

générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble de résidus basés sur la phase de porteuse, du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, du troisième ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance ;

dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir du premier ensemble d'ambiguïtés flottantes.

14. Procédé de la revendication 8, comprenant en outre les étapes consistant à :

générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble de résidus basés sur la phase de porteuse, du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, du troisième ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance ;

générer un premier ensemble d'ambiguïtés flottantes d'entier fixe pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble d'ambiguïtés flottantes ;

dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir du premier ensemble d'ambiguïtés flottantes d'entier fixe.

15. Procédé selon l'une des revendications précédentes, comprenant en outre les étapes consistant à :

obtenir un premier ensemble de premiers différentiels de retard ionosphérique associé aux signaux satellites reçus le long de la ligne de base formée par les première et deuxième stations de base, et

générer des corrections apportées à un ou plusieurs des résidus, les corrections étant liées au premier ensemble de premiers différentiels de retard ionosphérique, aux emplacements des première et deuxième stations de base, et à un emplacement estimé de la station itinérante ; et

modifier ledit un ou plusieurs des résidus avec lesdites corrections.

16. Procédé selon la revendication 8, comprenant en outre les étapes consistant à :

obtenir un premier ensemble de premiers différentiels de retard ionosphérique associé aux signaux satellites reçus le long de la ligne de base formée par les première et deuxième stations de base,

obtenir un deuxième ensemble de deuxièmes différentiels de retard ionosphérique associé aux signaux satellites reçus le long de la ligne de base formée par les première et troisième stations de base, et

générer des corrections apportées à un ou plusieurs des résidus, les corrections étant liées au premier ensemble de premiers différentiels de retard ionosphérique, au deuxième ensemble de deuxièmes différentiels de retard ionosphérique, aux emplacements des stations de base, et à un emplacement estimé de la station itinérante ; et

modifier ledit un ou plusieurs des résidus avec lesdites corrections.

17. Procédé de la revendication 16, dans lequel la correction apportée aux résidus associés au satellite "s" dans le deuxième ensemble de résidus et/ou le deuxième ensemble de résidus basés sur la phase de porteuse est liée à la quantité

où

est le premier différentiel de retard ionosphérique associé au satellite "s", et

est un différentiel de retard ionosphérique estimé associé au satellite "s" le long de la ligne de base entre la station itinérante et la première station de base.

18. Procédé de la revendication 16, dans lequel la correction apportée aux résidus associés au satellite "s" dans le troisième ensemble de résidus et/ou le troisième ensemble de résidus basés sur la phase de porteuse est liée à la quantité

où

est le deuxième différentiel de retard ionosphérique associé au satellite "s", et

est un différentiel de retard ionosphérique estimé associé au satellite "s" le long de la ligne de base entre la station itinérante et la première station de base.

19. Procédé de la revendication 16, dans lequel le différentiel de retard ionosphérique à partir du premier ensemble et associé au satellite "s" peut être indiqué par

dans lequel le différentiel de retard ionosphérique à partir du deuxième ensemble et associé au satellite "s" peut être indiqué par

dans lequel les emplacements des première, deuxième et troisième stations de base peuvent être représentés par les vecteurs X₁, X₂ et X₃, et dans lequel l'emplacement estimé de la station itinérante peut être représenté par X_0,k,
dans lequel les corrections apportées à un ou plusieurs des résidus associés au satellite "s" sont liées à une quantité

où


où α et β sont des constantes qui satisfont les relations :




où la notation {*}_n indique la composante de la quantité entre crochets le long de la direction nord, où la notation {*}_e indique la composante de la quantité entre crochets le long de la direction est.

20. Procédé de la revendication 19, dans lequel la correction apportée aux résidus associés au satellite "s" dans le deuxième ensemble de résidus et/ou le deuxième ensemble de résidus basés sur la phase de porteuse est liée à la quantité

où

est le premier différentiel de retard ionosphérique associé au satellite "s".

21. Procédé de la revendication 19, dans lequel la correction apportée au résidu associé au satellite "s" dans le troisième ensemble de résidus et/ou le troisième ensemble de résidus basés sur la phase de porteuse est liée à la quantité

où

est le deuxième différentiel de retard ionosphérique associé au satellite "s".

22. Procédé selon la revendication 16, comprenant en outre les étapes consistant à :

modifier un ou plusieurs des résidus ci-dessus pour qu'il(s) dépende(nt) des deuxième effets d'ordre dans les corrections de retard ionosphérique appliquées aux lignes de base associées à la station itinérante, et

générer une estimation des deuxièmes effets d'ordre, et

dans lequel l'étape (g) génère l'estimation de l'emplacement de la station itinérante davantage à partir des deuxièmes effets d'ordre estimés.

23. Procédé selon la revendication 16, dans lequel le procédé génère le premier ensemble de premiers différentiels de retard ionosphérique et le deuxième ensemble de deuxièmes différentiels de retard ionosphérique à partir d'au moins les données de navigation qu'il reçoit à partir des stations de base.

24. Procédé selon la revendication 16, comprenant en outre les étapes consistant à :

générer une estimation initiale du premier ensemble de premiers différentiels de retard ionosphérique associés aux signaux satellites reçus le long de la ligne de base formée par les première et deuxième stations de base ;

générer une estimation initiale du deuxième ensemble de deuxièmes différentiels de retard ionosphérique associés aux signaux satellites reçus le long de la ligne de base formée par les première et troisième stations de base ;

générer une estimation initiale d'un troisième ensemble de troisièmes différentiels de retard ionosphérique associés aux signaux satellites reçus le long de la ligne de base formée par les deuxième et troisième stations de base ; et

générer des estimations finales des différentiels de retard ionosphérique de telle sorte que la somme des estimations finales des premier, deuxième et troisième différentiels de retard ionosphérique pour au moins un satellite "s" autour d'une boucle des stations de base soit substantiellement égale à zéro.

25. Procédé de la revendication 7, dans lequel l'étape d'obtention du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite comprend l'étape de génération du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite à partir d'au moins les emplacements des stations de base et les données de navigation par satellite mesurées telles que reçues par les stations de base.

26. Procédé de la revendication 8, dans lequel l'étape d'obtention des premier et deuxième ensembles d'ambiguïtés de cycle de phase de porteuse de satellite comprend l'étape de génération du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite à partir d'au moins les emplacements des première et deuxième stations de base et les données de navigation par satellite mesurées telles que reçues par les première et deuxième stations de base, et l'étape de génération du deuxième ensemble d'ambiguïtés de cycle de phase de porteuse de satellite à partir d'au moins les emplacements des première et troisième stations de base et les données de navigation par satellite mesurées telles que reçues par les première et troisième stations de base.

27. Procédé de la revendication 26 comprenant en outre les étapes consistant à générer un troisième ensemble d'ambiguïtés de cycle de phase de porteuse de satellite associé à la ligne de base entre les deuxième et troisième stations de base, et à comparer la somme des trois ensembles d'ambiguïtés de phase de porteuse de satellite autour d'une boucle des stations de base à la valeur zéro.

28. Programme informatique qui, lorsqu'il est exécuté sur un processeur informatique, amène le processeur informatique à réaliser le procédé de l'une des revendications précédentes.

29. Appareil destiné à estimer l'emplacement d'une station itinérante (R) à l'aide d'une première station de base (B1) et d'une deuxième station de base (B2), l'appareil comprenant :

(a) un moyen pour recevoir les emplacements de la première station de base et de la deuxième station de base ;

(b) un moyen pour recevoir des données de navigation par satellite mesurées telles que reçues par la station itinérante, la première station de base, et la deuxième station de base ;

(c) un moyen pour obtenir un premier décalage temporel représentant une différence entre un premier décalage par rapport au temps GPS réel de l'horloge de la première station de base et un deuxième décalage par rapport au temps GPS réel de l'horloge de la deuxième station de base ;

(d) un moyen pour générer un premier ensemble de résidus d'équations de navigation différentielles associé à une première ligne de base (R-B1) entre la station itinérante et la première station de base, les résidus étant liés aux données de navigation par satellite mesurées qui sont reçues par la station itinérante et la première station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la première station de base ;

(e) un moyen pour générer un deuxième ensemble de résidus d'équations de navigation différentielles associé à une deuxième ligne de base (R-B2) entre la station itinérante et la deuxième station de base, les résidus étant liés aux données de navigation par satellite mesurées qui sont reçues par la station itinérante et la deuxième station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la deuxième station de base ; et

(f) un moyen pour remplacer, dans le deuxième ensemble de résidus, un décalage temporel inconnu associé à la deuxième ligne de base (R-B2) par une valeur composée d'une somme du premier décalage temporel et d'un décalage temporel associé à la première ligne de base (R-B1) ; et

(g) un moyen pour générer, à la suite de la substitution de l'étape (f), une estimation de l'emplacement de la station itinérante à partir du premier ensemble de résidus, du deuxième ensemble de résidus et du premier décalage temporel.

30. Appareil de la revendication 29 comprenant en outre :

(h) un moyen pour recevoir l'emplacement de la troisième station de base;

(i) un moyen pour recevoir des données de navigation par satellite mesurées telles que reçues par la troisième station de base ;

(j) un moyen pour obtenir un deuxième décalage temporel représentant la différence entre le premier décalage par rapport au temps GPS réel de l'horloge de la première station de base et un troisième décalage par rapport au temps GPS réel de l'horloge de la troisième station de base ;

(k) un moyen pour générer un troisième ensemble de résidus d'équations de navigation différentielles associé à une troisième ligne de base (R-B3) entre la station itinérante et la troisième station de base, les résidus étant liés aux données de navigation par satellite reçues par la station itinérante et la troisième station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la troisième station de base ;

(1) un moyen pour remplacer, dans le troisième ensemble de résidus, un décalage temporel inconnu associé à la troisième ligne de base (R-B3) par une valeur composée d'une somme du deuxième décalage temporel et d'un temps associé à la première base (R-B1) ; et

dans lequel le moyen (g) de génération, à la suite de l'étape de substitution (1), de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du troisième ensemble de résidus et du deuxième décalage temporel.

31. Appareil de la revendication 29, dans lequel le moyen (c) d'obtention du premier décalage temporel comprend un moyen de génération du premier décalage temporel.

32. Appareil de la revendication 30, dans lequel le moyen (c) d'obtention du premier décalage temporel comprend un moyen de génération du premier décalage temporel et dans lequel le moyen (j) d'obtention du deuxième décalage temporel comprend un moyen de génération du deuxième décalage temporel.

33. Appareil de la revendication 32, comprenant en outre un moyen pour générer un troisième décalage temporel représentant la différence temporelle entre le deuxième décalage par rapport au temps GPS réel de l'horloge de la deuxième station de base et le troisième décalage par rapport au temps GPS réel de l'horloge de la troisième station de base, et un moyen pour comparer la somme du premier décalage temporel, du deuxième décalage temporel, et du troisième décalage temporel autour d'une boucle des stations de base à la valeur zéro.

34. Appareil de la revendication 29 ou 30, dans lequel les premier et deuxième ensembles de résidus sont basés sur des données de pseudo-distance, et dans lequel l'appareil comprend en outre un moyen pour générer un premier ensemble de résidus basés sur la phase de porteuse d'équations de navigation différentielles pour la première ligne de base (R-B1) entre la station itinérante et la première station de base, le premier ensemble de résidus basés sur la phase de porteuses étant lié à au moins les données de phase de porteuse de satellite mesurées qui sont reçues par la station itinérante et la première la station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la première station de base ; et
dans lequel le moyen (g) de génération de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du premier ensemble de résidus basés sur la phase de porteuse.

35. Appareil de la revendication 34 comprenant en outre :

un moyen pour obtenir un premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite associé à la ligne de base entre les première et deuxième stations de base ;

un moyen pour générer un deuxième ensemble de résidus basés sur la phase de porteuse d'équations de navigation différentielles associé à la deuxième ligne de base (R-B2) entre la station itinérante et la deuxième station de base, le deuxième ensemble de résidus basés sur la phase de porteuse étant lié à au moins les données de phase de porteuse de satellite mesurées qui sont reçues par la station itinérante et la deuxième station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la deuxième station de base ; et

dans lequel le moyen (g) de génération de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du deuxième ensemble de résidus basés sur la phase de porteuse et du premier ensemble d'ambiguïtés de cycle de phase de satellite.

36. Appareil de la revendication 35, dans lequel la revendication 34 est dépendante de la revendication 30 comprenant en outre :

un moyen pour obtenir un deuxième ensemble d'ambiguïtés de cycle de phase de porteuse de satellite associé à la ligne de base entre les première et troisième stations de base ;

un moyen pour générer un troisième ensemble de résidus basés sur la phase de porteuse d'équations de navigation différentielles associé à la troisième ligne de base (R-B3) entre la station itinérante et la troisième station de base, le troisième ensemble de résidus basés sur la phase de porteuse étant lié à au moins les données de phase de porteuse de satellite mesurées qui sont reçues par la station itinérante et la troisième station de base, les emplacements des satellites, et les emplacements de la station itinérante et de la troisième station de base ; et

dans lequel le moyen (g) de génération de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du troisième ensemble de résidus basés sur la phase de porteuse et du deuxième ensemble d'ambiguïtés de cycle de phase de satellite.

37. Appareil de la revendication 32, comprenant en outre un moyen pour générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance; et
dans lequel le moyen (g) de génération de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du premier ensemble d'ambiguïtés flottantes.

38. Appareil de la revendication 34 comprenant en outre :

un moyen pour générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance; et

un moyen pour générer un premier ensemble d'ambiguïtés flottantes d'entier fixe pour la ligne de base entre la station itinérante et la première station de base du premier ensemble d'ambiguïtés flottantes ;

dans lequel le moyen (g) de génération d'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du premier ensemble d'ambiguïtés flottantes d'entier fixe.

39. Appareil de la revendication 35 comprenant en outre :

un moyen pour générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble de résidus basés sur la phase de porteuse, du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance ;

dans lequel le moyen (g) de génération de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du premier ensemble d'ambiguïtés flottantes.

40. Appareil de la revendication 35 comprenant en outre :

un moyen pour générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble de résidus basés sur la phase de porteuse, du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance ; et

un moyen pour générer un premier ensemble d'ambiguïtés flottantes d'entier fixe pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble d'ambiguïtés flottantes ;

dans lequel le moyen (g) de génération de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du premier ensemble d'ambiguïtés flottantes d'entier fixe.

41. Appareil de la revendication 36 comprenant en outre :

un moyen pour générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble de résidus basés sur la phase de porteuse, du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, du troisième ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble d'ambiguïtés de cycle de phase de porteuse de satellite liés à la ligne de base entre les première et deuxième stations de base, et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance ;

dans lequel le moyen (g) de génération de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du premier ensemble d'ambiguïtés flottantes.

42. Appareil de la revendication 36 comprenant en outre :

un moyen pour générer un premier ensemble d'ambiguïtés flottantes pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble de résidus basés sur la phase de porteuse, du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, du troisième ensemble de résidus basés sur la phase de porteuse, du deuxième ensemble d'ambiguïtés de cycle de phase de porteuse de satellite lié à la ligne de base entre les première et deuxième stations de base, et d'au moins l'un des ensembles de résidus basés sur des données de pseudo-distance ; et

un moyen pour générer un premier ensemble d'ambiguïtés flottantes d'entier fixe pour la ligne de base entre la station itinérante et la première station de base à partir du premier ensemble d'ambiguïtés flottantes ;

dans lequel le moyen (g) de génération de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir du premier ensemble d'ambiguïtés flottantes d'entier fixe.

43. Appareil selon l'une des revendications précédentes 29-42 comprenant en outre :

un moyen pour obtenir un premier ensemble de premiers différentiels de retard ionosphérique associé aux signaux satellites reçus le long de la ligne de base formée par les première et deuxième stations de base, et

un moyen pour générer des corrections apportées à un ou plusieurs des résidus, les corrections étant liées au premier ensemble de premiers différentiels de retard ionosphérique, aux emplacements des première et deuxième stations de base, et à un emplacement estimé de la station itinérante ; et

un moyen pour modifier lesdits un ou plusieurs des résidus avec lesdites corrections.

44. Appareil selon la revendication 36 comprenant en outre :

un moyen pour obtenir un premier ensemble de premiers différentiels de retard ionosphérique associé aux signaux satellites reçus le long de la ligne de base formée par les première et deuxième stations de base,

un moyen pour obtenir un deuxième ensemble de deuxièmes différentiels de retard ionosphérique associé aux signaux satellites reçus le long de la ligne de base formée par les première et troisième stations de base, et

un moyen pour générer des corrections apportées à un ou plusieurs des résidus, les corrections étant liées au premier ensemble de premiers différentiels de retard ionosphérique, au deuxième ensemble de deuxièmes différentiels de retard ionosphérique, aux emplacements des stations de base, et à un emplacement estimé de la station itinérante ; et

un moyen pour modifier lesdits un ou plusieurs des résidus avec lesdites corrections.

45. Appareil de la revendication 44, dans lequel la correction apportée aux résidus associés au satellite "s" dans le deuxième ensemble de résidus et/ou le deuxième ensemble de résidus basés sur la phase de porteuse est liée à la quantité

où

est le premier différentiel de retard ionosphérique associé au satellite "s", et

est un différentiel de retard ionosphérique estimé associé au satellite "s" le long de la ligne de base entre la station itinérante et la première station de base.

46. Appareil de la revendication 44, dans lequel la correction apportée aux résidus associés au satellite "s" dans le troisième ensemble de résidus et/ou le troisième ensemble de résidus basés sur la phase de porteuse est liée à la quantité

où

est le deuxième différentiel de retard ionosphérique associé au satellite "s", et

est un différentiel de retard ionosphérique estimé associé au satellite "s" le long de la ligne de base entre la station itinérante et la première station de base.

47. Appareil de la revendication 44, dans lequel le différentiel de retard ionosphérique à partir du premier ensemble et associé au satellite "s" peut être indiqué par

dans lequel le différentiel de retard ionosphérique à partir du deuxième ensemble et associé au satellite "s" peut être indiqué par

dans lequel les emplacements des première, deuxième et troisième stations de base peuvent être représentés par les vecteurs X₁, X₂ et X₃, et dans lequel l'emplacement estimé de la station itinérante peut être représenté par X_0,k,
dans lequel les corrections apportées à l'un ou plusieurs des résidus associés au satellite "s" sont liées à une quantité

où


où α et β sont des constantes qui satisfont les relations :



où la notation {*}_n indique la composante de la quantité entre crochets le long de la direction nord, où la notation {*}_e indique la composante de la quantité entre crochets le long de la direction est.

48. Appareil de la revendication 44, dans lequel la correction apportée aux résidus associés au satellite "s" dans le deuxième ensemble de résidus et/ou le deuxième ensemble de résidus basés sur la phase de porteuse est liée à la quantité

où

est le premier différentiel de retard ionosphérique associé au satellite "s".

49. Appareil de la revendication 44, dans lequel la correction apportée au résidu associé au satellite "s" dans le troisième ensemble de résidus et/ou le troisième ensemble de résidus basés sur la phase de porteuse est liée à la quantité

où

est le deuxième différentiel de retard ionosphérique associé au satellite "s".

50. Appareil selon la revendication 43 comprenant en outre :

un moyen pour modifier un ou plusieurs des résidus ci-dessus pour qu'il(s) dépende(nt) des deuxièmes effets d'ordre dans les corrections de retard ionosphérique appliquées aux lignes de base associées à la station itinérante, et

un moyen pour générer une estimation des deuxièmes effets d'ordre, et

dans lequel le moyen (i) de génération de l'estimation de l'emplacement de la station itinérante génère l'estimation davantage à partir des deuxièmes effets d'ordre estimés.

51. Dispositif selon la revendication 43, dans lequel l'appareil génère le premier ensemble de premiers différentiels de retard ionosphérique et le deuxième ensemble de deuxièmes différentiels de retard ionosphérique à partir d'au moins les données de navigation qu'il reçoit à partir des stations base.

52. Appareil selon la revendication 43 comprenant en outre :

un moyen pour générer une estimation initiale du premier ensemble de premiers différentiels de retard ionosphérique associé aux signaux satellites reçus le long de la ligne de base formée par les première et deuxième stations de base ;

un moyen pour générer une estimation initiale du deuxième ensemble de deuxièmes différentiels de retard ionosphérique associé aux signaux satellites reçus le long de la ligne de base formée par les première et troisième stations de base ;

un moyen pour générer une estimation initiale d'un troisième ensemble de troisièmes différentiels de retard ionosphérique associé aux signaux satellites reçus le long de la ligne de base formée par les deuxième et troisième stations de base ; et

un moyen pour générer des estimations finales des différentiels de retard ionosphérique de telle sorte que la somme des estimations finales des premier, deuxième et troisième différentiels de retard ionosphérique pour au moins un satellite "s" autour d'une boucle de la station de base soit essentiellement égale à zéro.

53. Appareil de la revendication 35, dans lequel le moyen d'obtention du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite comprend un moyen de génération du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite à partir d'au moins les emplacements des stations de base, et les données de navigation par satellite mesurées telles que reçues par les stations de base.

54. Appareil de la revendication 36, dans lequel le moyen d'obtention des premier et deuxième ensembles d'ambiguïtés de cycle de phase de porteuse de satellite comprend un moyen de génération du premier ensemble d'ambiguïtés de cycle de phase de porteuse de satellite à partir d'au moins les emplacements des première et deuxième stations de base et des données de navigation par satellite mesurées telles que reçues par les première et deuxième stations de base, et un moyen de génération du deuxième ensemble d'ambiguïtés de cycle de phase de porteuse de satellite à partir d'au moins les emplacements des première et troisième stations de base et des données de navigation par satellite mesurées telles que reçues par les première et troisième stations de base.

Drawing